Full Idea
The problem of induction is (roughly) finding a way to prove that certain empirical generalisations which are derived from past experience will hold good also in the future.
Gist of Idea
The induction problem is to prove generalisations about the future based on the past
Source
A.J. Ayer (Language,Truth and Logic [1936], Ch.2)
Book Reference
Ayer,A.J.: 'Language, Truth and Logic' [Penguin 1974], p.66
A Reaction
This doesn't seem to be the only problem. It seems self-evident (since Hume) that you cannot use deductive reasoning to prove that the future will be like the past. In fact, we should obviously be cautious, as things could easily change.