Jehovah's Witnesses's teaching on the Church I just read a wiki page on Jehovah's witnesses, visited their official website, and was quite surprised that in the list of their believes there is a striking absence of the definition (or at least description) of their concept of the Church. 

According to what I can see at the moment, they are only using the word "church" or plural "churches" in reference to the numerous religious groups in the main-stream Christianity (which they consider all to be in apostasy), while they themselves prefer to speak about the Kingdom, rather than the Church. 

Is it a result of their special translation of the Bible (in which many words were translated quite differently from the way it is done in the majority of Bible translations, for example, in many places the word that is translated in other translations as "fellowship" in their translation is rendered as "sharing") or am I simply missing out on something here?

What's their concept of the Church? What's their teaching on the Church? When did it start? How long has it been around? Has it always existed since it was started or, perhaps, it was over at some time and then re-stated again?
The word church has various meanings. It can be used to refer to an physical building. Witness churches are called Kingdom Halls. It can also be used to refer to a group of believers in a specific area. For sense of the word, Witnesses use congregation, which I believe is quite common for many branches of Christianity.

But the word church has another meaning, and it is this meaning I think you're asking about. The "church" as the united body of all believers. For this sense, Witnesses don't have a direct word. They do use the word Christian in a very narrow sense, to refer only to themselves. Perhaps that's their nearest equivalent. And yes, they do believe that "true Christianity" essentially died out after the First Century, and (with the exception of a few brief flames here and there) was reborn with them.

The church may also be the organisation, the institution, as distinct from the individual members thereof. For that sense, the Witnesses use various words, notably, the word organisation itself. They may also talk of the "Faithful and Discreet Slave", which is the teaching body of the organisation (basically, the group that define the doctrine).

The finer points of how the Faithful and Discreet Slave is distinct from the Governing Body have now escaped me. I used to know that. I've forgotten.