Adware is the term given to software that is free to download because it has (sometimes intrusive) ads that pay the bills for the developer.
Nowadays, most adware programs come in the form of "toolbars," which are added to your web browser and take over the search engine and homepage. AOL, Yahoo, Bing and Google all have toolbars that are sometimes included with popular adware.
Adware is safe if downloaded from reputable sites (like Afterdawn) and from reputable developers.
The software and ads can be turned malicious and into keyloggers, which take note of your keystrokes, searching for passwords and other personal info.
Make sure, as with all software, to have an anti-virus installed.
Related software tools
CCleaner is a freeware system optimization and privacy tool.