Actually, the accepted answer is technically wrong. I say technically wrong, because it's a bug that means that completing the bards quest does nothing, when actually you should get a bonus to your speech learning.
You're supposed to get the Active Effect 'Gift of the Gab', which lets you develop Speech 15% faster, but it doesn't activate because of yet another bug.
See the bugs section herehere. Hopefully this'll get fixed in a future patch and will work retroactively for those who've already completed the questline.