Consumer surplus is basically the difference between what you are willing to pay for something and the price you actually pay for it, the consumer's gain from trade. (Do not confuse consumer surplus with utitily; consumer surplus has a definite dollar value, but utility does not, as WoOs explains in his well-written node)

For example, today I bought a new book for $17. I was willing to pay a maximum of $20 for the book, so I earned a consumer surplus of $3. I walked out of the store $3 richer than I walked in; I walked out with merchandise I valued at $20 but I had only paid $17 for it.

Consumer surplus is closely related to producer surplus (basically if the book had cost $18, you would have had one less dollar of surplus but the producer/seller would have had one more.) Click here to see how you can talk about welfare and surplus to make an argument against taxes.

prices  |              supply curve
        | \    \       /
        |a \ b  \     /
      p1|___\____\   /
        |  c \d | \ /
        | f   \g|h/|\
      p3|_______|/ | \
        |       /\ |  \
        | PS   /| \|   \
        |     / |  \    \
        |    /  |  |\    \
        |   /   |  | \    \
        |  /    |  |  \    \
        | /     |  |   \    \
        |/      |  |    \    original demand curve
        |       |  |     \
        |       |  |      demand curve with tax  
                q1 q2     quantity 

Without the tax, the consumer has the area above price below demand as consumer surplus. The producer has the area below price above supply. Before the demand curve drops due to the tax, we are opperating along the upper demand curve, so consumer surplus is (a + b + c + d + e) and producer surplus is (f + g + h + PS).

Once the tax is in place, fewer items are sold (quantity sold drops from q1 to q2). The tax money is not a deadweight loss; if we assume the government is not wasting the money (doing something that does not improve anyone's welfare anywhere), then the welfare from that money is going somewhere. If they give the revenues from the sales tax to someone on social security, then that person is exactly as much better off as the consumer and producer are worse off, and there is no net loss to society. (If you believe the government is using your money to roll joints, there is a definite deadweight loss there.)

With the tax, consumer surplus drops to a + b and producer surplus is simply PS. The area (c + d + f + g) goes as tax revenue. However, area ( e + h) is still a deadweight loss; without the tax someone was receiving that benefit and now no one is.