Well back in the day what my church now calls General Assembly was known as the Holy Convocation. I believe COGIC does this too, and both of our organizations are Pentecostal.
Ours was/is basically a gathering of every member of the organization to one location for 7-10 days of church services, prayer, seminars and business meetings. At the business meetings we (Ministers, Elders, Pastors, Evangelists, and Bishops) vote on different by-laws and policies, as well as learn more information about any developments that the organization has made or is a part of. Seminars cover a wide range of topics from Bible Enrichment for young men and women, to ministry of music, ushering, vacation bible school (in which I'm a teacher), exogesis of scripture, etc...
Church services are the best part lol! We are pretty traditional, so we have Praise & Worship, Testimony Service (it is loooonnng, but they try to limit it to blessings, healings, miracles that happened during the week...), a lot of solos, choirs, etc. I generally play during our Youth and Brotherhood services...
That's all I can think of that is pertinent. I don't know the origins of the term though, a little research is in order.