This is the name given to one mode of creating presumably valid propositions: you consider many known true facts, and form a general rule which predicts all those facts.
For example, we have the facts: (1)today the sun rose, (2)yesterday the sun rose, (3)the day before yesterday the sun rose, ..., (N)the day I was born the sun rose. From these, we can use scientific induction to form the proposition the sun rises every day.
Scientific induction, of course, gets its name because it is assumed to be the basis for the scientific method. (Although there is not complete agreement that that is in fact the case). It is the "opposite" of deduction, which starts with a general rule, and derives specific instances of it. (e.g., "all men are mortal, and Socrates is a man, so Socrates is mortal").
The problem of induction is: why should we trust scientific induction to give valid results? Unlike deduction, it is not logically necessary. Even more disturbingly, it is not even "inductively" necessary -- we can give many examples where inductions does work, but also many where it does not! And yet, many of the facts we feel most certain about are rooted in induction.
Scientific induction should not be confused with mathematical induction, which is a type of deduction.