Freeware is software made available for public use by the author, and it's free. You're not under any obligation to pay for it. Freeware is usually distributed in the same places you find shareware and public domain software: on bulletin boards, at user groups, and by commercial shareware distributors.
The difference between freeware and public domain software (which is also free) is that the freeware author retains the copyright to the software. Because of this you cannot do anything with the software that the author doesn't allow you to. For example, you can't distribute it for profit, and you can't incorporate it into other programs, unless the author gives permission. Public domain software, by contrast, is given over in its entirety to the public domain with no strings attached. As for shareware, you should see that entry.