What are the theological implications of "filioque"? Depending on your tradition, the Nicene Creed may or may not say that the Holy Spirit proceeds from the Son as well as from the Father:


  (Greek) τὸ ἐκ τοῦ πατρὸς ἐκπορευόμενον - who from the Father proceeds 
  (Latin) qui ex Patre Filioque procedit - who from the Father and the Son proceeds


This has been a point of contention between the Orthodox and Western churches, the latter category including both Catholics and Protestants, for at least a thousand years, contributing to the Great Schism. I have read about the history of "filioque" but I have basically no idea what the theological difference is meant to be. I understand that there is some doubt about whether "ἐκπορευόμενον" means the same thing as "procedit", so both versions could be right (and apparently we all agree it would be wrong to insert "and the Son" into the Greek) but I don't see what either version of "proceeding" is meant to imply about the nature of the Trinity.

If the Spirit proceeds from the Father and the Son, or from the Father alone, what does that actually mean for our understanding of God?
The filioque is meant as a theological explanation of the relationship between the Spirit and the Son. The Bible tells us that the Son is begotten from the Father, and that the Spirit proceeds from the Father, but any curious Trinitarian is going to wonder what the Spirit-Son relationship is. And the West, as a rule, is much more interested in nailing down theological specifics than the East.

As far as theology following from it, the filioque has led some western theologians to suggest that the Holy Spirit is the love between the Father and the Son, a love so strong that it is an actual person, which is an interesting thought.

The Orthodox have some doctrinal objections to it, largely that it makes the Holy Spirit a subordinate or less important member of the Trinity:


  The filioque distorts Orthodox Triadology by making the Spirit a
  subordinate member of the Trinity. Traditional Triadology consists in
  the notion that for any given trait, it must be either common to all
  Persons of the Trinity or unique to one of them. Thus, Fatherhood is
  unique to the Father, while begottenness is unique to the Son, and
  procession unique to the Spirit. Godhood, however, is common to all,
  as is eternality, uncreatedness, and so forth. Positing that something
  can be shared by two Persons (i.e., being the source of the Spirit's
  procession) but not the other is to elevate those two Persons at the
  expense of the other. Thus, the balance of unity and diversity is
  destroyed.


Historically, though, the contention has been at least as much about church authority as it has been about theology. The original creed (from the ecumenical councils at Nicea and Constantinople) did not include the filioque, and when the bishop of Rome unilaterally sanctioned its use, Eastern bishops saw that as something totally outside his authority to do.