Deductive reasoning is the process of reasoning from general premises to specific conclusions.  This is in contrast to inductive reasoning, in which a person takes specific facts and uses them to reach general conclusions.

To illustrate this, let us look at an example.  Deductive arguments will often have two premises and a conclusion.  Premise 1: All birds have two legs.  Premise 2: A penguin is a bird.  Conclusion: A penguin has two legs. 

Here, we have general statements about birds and penguins, and we use them to deduce a specific conclusion about penguins.

A deductive argument is valid if it is impossible for the conclusion to be false if the premises are true.  Therefore, the previous argument was valid.  If it is true that all birds have two legs and that penguins are birds, it must be true that a penguin has two legs.

A deductive argument is sound if it is valid AND the premises are true.  Therefore, an argument can be valid, but not sound.  However, it cannot be sound without being valid.

An argument that is valid but not sound might go like this:

Premise 1: All houses are pink.  Premise 2: That structure is a house.  Conclusion: That structure is pink.

This conclusion follows from the premises and is therefore valid.  However, not all houses are pink so Premise 1 is false and the argument is not sound.