A simple google earth search turns up hundreds of "First Congregational Churches" all over the U.S. What is the significance of this name?
Assuming you don't know about Congregationalism
Congregationalism is a system of governance where the local church independently and autonomously runs its own affairs. It does not specify any doctrine or hierarchy, which allows for the existence of 'Methodist Congregational' churches and 'Uniting Congregational' churches. There are two major denominations in the US which are Congregational throughout their structure - the 'National Association of Congregational Christian Churches' and the 'Conservative Congregational Christian Conference'.
Congregational churches are usually Protestant although there are also Congregationalist variants of other religious institutions.
As for the "first" bit
I haven't been able to track down any conclusive evidence.
Wikipaedia lists approximately 100 churches called "First Congregational Church" and only 2 called "Second Congregational Church". They are all in the US.
Congregational churches are part of the Puritan tradition. The English Puritans, who formed a really core part of the New England colonies, distanced themselves from traditional (high) church practice, especially when these were the same as Roman Catholic practices that they disagreed with.
In traditional Christian practice – this definitely dates back to the fourth century (see list of oldest church buildings) – churches were dedicated to a particular saint, or event in the life of Christ (or the Virgin Mary), or some aspect of God. Often, the church might actually be built or house the remains (relics) of the saint to which it is dedicated.
The seventeenth-century Puritans disagreed with this practice, as do their present-day successors. You may see some churches in this or similar streams of tradition named after Christian concepts such as Trinity or Grace, but equally common are neutral names based on the location of the church. “First,” apparently, is a pretty obvious choice for the first church in a particular location, if that location is a large city.