Para churches are church-like organizations that aren't technically churches in the traditional sense (of Sunday suits and buildings with pews), but function very much similar to the traditional churches. They meet during the week to sing praise songs, study the Bible, and fellowship. They usually do not take the place of a normal church (and they shouldn't,) but they do supplement a church in providing a program during the week when traditional churches often do not meet, and providing a place for people of different churches to meet.
Para-churches often meet at one of the members' house, in public places, or sometimes in rented buildings. Besides the singing, studying, and fellowshipping, they may also do other activities -- trips, public performance, parties, etc.
Because para-churches can take the place of a church, or sometimes even turn into a cult, some people discourage participating in such groups. On the other hand, when run by a group of responsible people they can be very useful in strengthening one's faith. If you're looking for such group, I recommend joining a group with a national reputation and/or ones sponsored by a local church, not some small random groups or fads that happens to be in the area.