The grouping Ural-Altaic was a theory from the late 1800s that was in favor until about 1960, but is no longer accepted. But the two groups are still considered valid.
Ural languages include Finnish, Hungarian, and their Finno-Ugric predecessors, plus Samoyedic.
Altaic languages include Turkic, Mongolic, and Tungusic. Put all this together, and you have the group once called the Ural-Altaic languages. You can get the whole story at http://en.wikipedia.org/wiki/Ural%E2%80%93Altaic_l... .