Note that many websites have their own advertising, unrelated to adware.
A Browser Helper Object, or BHO, is just a small program that runs automatically every time you start your Internet browser. Usually, a BHO is installed on your system by another software program. For example, Go!Zilla, the downloading utility, used to install a BHO created by Radiate (formerly Aureate Media); this BHO tracks which advertisements you see as you surf the Web.
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The natural question is, what do BHOs do? The technical answer is "anything", but generally, it will have something to do with helping you browse the Internet. Of course, some BHOs are what is called "ad-ware" or "spyware": they do things like monitor the websites you visit and report this data back to their creators.