Page 4 

The True Purpose of Speaking in Tongues

So what is the purpose for this gift?  Paul goes on to clearly define what this gift is for:

In the Law it is written, “BY MEN OF STRANGE TONGUES AND BY THE LIPS OF STRANGERS I WILL SPEAK TO THIS PEOPLE, AND EVEN SO THEY WILL NOT LISTEN TO ME,” says the Lord. So then tongues are for a sign, not to those who believe but to unbelievers; but prophecy is for a sign, not to unbelievers but to those who believe. (1Co 14:21-22 NASB)

Tongues are for a sign to unbelievers as was shown on the day of Pentecost, intended for the conviction and conversion of non-Christians.  The gift was necessary to spread Christianity and build churches.  It was intended to convince unbelievers of the doctrine that Christians had already embraced.  Prophecy, and interpreting scripture in their own language, is what was used for the edification of the church.  This is why Paul said that they should desire prophecy:

Pursue love, yet desire earnestly spiritual gifts, but especially that you may prophesy. (1Co 14:1 NASB)

As Matthew Henry says;

That gifts may be rightly used, it is proper to know the ends which they are intended to serve. To go about the conversion of infidels, as the apostles did, had been a vain undertaking without the gift of tongues, and the discovery of this gift; but, in an assembly of Christians already converted to the Christian faith, to make use and ostentation of this gift would be perfectly impertinent, because it would be of no advantage to the assembly; not for conviction of truth, because they had already embraced it; not for their edification, because they did not understand, and could not get benefit without understanding, what they heard. – Matthew Henry’s Commentary on the Whole Bible.