Deductive reasoning is a type of reasoning that starts out with one or more claims (the premises) and concludes with a different claim (the conclusion) whose truth is guaranteed by the validity of the reasoning process. Inductive reasoning, on the other hand, starts out with one or more premises and tries to generalize from what is true in some cases to what is likely to be true in general.
Deductive reasoning makes use of the rules of logic to arrive to a conclusion. If the premises are true and the laws applied are correct, then the conclusion is necessarily true as well. This is an example of deductive reasoning: "All men are mortal. Socrates is a man. Therefore, Socrates is mortal." The conclusion ("Socrates is mortal") is derived from the two premises ("All men are mortal" and "Socrates is a man") by applying the law from predicate logic called Universal Instantiation.
In inductive reasoning, the role of the premises is to provide strong support to the conclusion, but the truth of the conclusion is not guaranteed, because this kind of reasoning does not use universal laws (such as the laws of logic) to reach the conclusion. The following piece of reasoning is inductive: "I have seen many swans and they were all white. Therefore, all swans are white." In this case, the reasoning is correct because the premise supports the conclusion, but the conclusion is false, since there are black swans.