From a Fundamentalist standpoint, what does the phrase "Inspired, infallible, inerrant Word of God" mean? Many denominations teach that the Bible is the "inspired, inerrant, infallible Word of God."  Detractors of Christianity, and even some denominations within Christianity, disagree with all or some of those three descriptions.  Quite often, they counter with examples of errors in the Bible, or in various translations that show errors (such as the Wicked Bible's translation of Exodus 20:14).

Various questions and answers on this site have touched on one or all of these three statements, but we've yet to have an answer that describes how all three of these Biblical statements relate to each other, and to the nature of Scriptures.  Granted, there are different understandings, and per the site guidelines, I want to keep this scoped to the classic Fundamentalist understanding of the statement - namely that of the Churches and traditions that hold that the Bible is the inspired, inerrant Word of God.  

I want to have this in layman's terms, in order to address the straw-man arguments leveled against the statement.
As noted in the question, these are layman's terms.  However, I am providing links to more official definitions, which have been used as source material.

Definition of the term "Inspired": The doctrine of the inspiration of the Bible means that the Bible in the original documents is God-breathed, that it is a divine product, and, because it is divine, the original documents are inerrant.


"inspired" does not mean "inspired" in the common sense, as in an artist is inspired to produce a great work, or a football team is inspired to perform better than normal due to a very motivational speech. In the doctrine of Divine Inspiration, the term carries the connotation that the words are the actual words of God.
Many cite 2 Timothy 3:16 as the source for the term "inspired".  The term "God Breathed" is translated from the Greek word "Theopneustos", which conveys the idea of God directly filled the writer with the necessary knowledge - the God breathed the knowledge into the writer.
From Clarke's Commentary on the Bible, we get two possible meanings for the idea of how this worked:


That every thought and word were inspired by God, and that the writer did nothing but merely write as the Spirit dictated.
That God gave the whole matter, leaving the inspired writers to their own language; and hence the great variety of style and different modes of expression.  (This is the understanding that is most common in Baptist Churches in particular, and in most Fundamentalist Churches in my admittedly limited experience.)

There are many, many verses in Scripture, other than 2 Timothy 3:16, that claim that the Bible is the direct Word of God, not that of man.  A more full treatment, including lists of such passages can be found at gospelgateway.com: 
Note that inspiration and inerrancy are intertwined, but more specifically that they apply to the original documents.  Neither quality is attributed to translations o
and/or the copies of the original documents.  
This leaves open the question of whether the translations we have today, all of which are based on copies, have been accurately transmitted through history.  Fortunately, we can answer that with a resounding "Yes, we can be very confident that what we have today is a fair representation of the original manuscripts".
It does mean that the Bible is the Word of God, not that it contains the Word of God.


Definition of "Inerrant": The doctrine of inerrancy stems from  the doctrine of inspiration.  Simply put, if all Scripture is indeed of God, then it cannot be erroneous.  God, being perfect, cannot make mistakes, and He has the power to ensure the original writers wrote down exactly what He intended.  A much fuller and more detailed exposition can be found in the Chicago Statement on Biblical Inerrancy.


Again, as with Inspiration, the doctrine of inerrancy applies only to the original autographs, not to copies and translations.
The doctrine of inerrancy does not imply hyper-literalism.  As noted above, in the second possible mechanism for Biblical Inspiration, we believe God allowed the writer's literary style to be used in the writing of Scripture.  Hyperbole (the use of exaggeration as a figure of speech.  Example, "I'm so hungry, I could eat a horse.") is allowed.
It also does not imply that our interpretation (understanding) of Scripture is necessarily without error.  Verses taken out of context, differences in understanding of meaning and original phrases, cultural differences, and misunderstanding of the meaning of certain phrases at the time the original document was written can (and have) led to many disagreements over the meaning of Scripture.


Infallible has a stronger meaning than inerrant.  Inerrant means the Bible contains no errors.  Infallibility means it cannot contain errors; that is, it would not be possible.  Again, this concept is a direct result of the doctrine of inspiration.  The Bible cannot contain errors because it is wholly the inspired word of God.



Taken together, the statements do not mean we believe that we have a perfect understanding of Scripture.  They do not mean our current Scriptures are perfect, even if we remove our imperfect comprehension and understanding from the equation.

So, what does the phrase "The Bible is the Inspired, Inerrant Word of God" mean to a Fundamentalist?

In simple terms it means God's Word was originally, accurately, and perfectly recorded by the prophets, kings, peasants, fishermen, political leaders, a tax collector, a rabbi, a cupbearer, and ministers that God used.  It was originally perfect, through God's divine power.

Combined with the evidence that we have that it was, for the most part, transmitted accurately through time, and the high degree of confidence we have in the reliability of today's manuscripts, the phrase tells us we can trust the Scripture we have.  It is therefore up to study it, understand it, and weed out erroneous teachings.  As Christians, we have a responsibility to understand correct doctrine because God has provided us with the information we need to do so.  The phrase means God's word is indeed profitable for teaching, rebuking, correcting and training in righteousness, that the man of God may be perfect, throughly furnished unto all good works.



I wanted to include this summary, from the Chicago Statement on Biblical Inerrancy but it didn't quite fit in with the above answer, as it's not really "Layman's Terms".  It is clear and concise, however.


  
  God, who is Himself Truth and speaks truth only, has inspired Holy Scripture in order thereby to reveal Himself to lost mankind through
  Jesus Christ as Creator and Lord, Redeemer and Judge. Holy Scripture
  is God's witness to Himself.
  
  
  Holy Scripture, being God's own Word, written by men prepared and superintended by His Spirit, is of infallible divine authority in all
  matters upon which it touches: It is to be believed, as God's
  instruction, in all that it affirms; obeyed, as God's command, in all
  that it requires; embraced, as God's pledge, in all that it promises.
  The Holy Spirit, Scripture's divine Author, both authenticates it to us by His inward witness and opens our minds to understand its
  meaning.
  Being wholly and verbally God-given, Scripture is without error or fault in all its teaching, no less in what it states about God's acts
  in creation, about the events of world history, and about its own
  literary origins under God, than in its witness to God's saving grace
  in individual lives.
  The authority of Scripture is inescapably impaired if this total divine inerrancy is in any way limited of disregarded, or made
  relative to a view of truth contrary to the Bible's own; and such
  lapses bring serious loss to both the individual and the Church.