To eradicate something is to get rid of it, to destroy it, and to kiss it goodbye.
Eradicate is from the Latin word eradicare meaning "to root out." When you yank that weed up by the roots, it has been eradicated; it's not coming back. Eradicate often means to kill a bunch of somethings, like what you want the poison to do to the roach family and their extended relatives living in your house, and what we thought we did to bedbugs. You can also eradicate corruption, poverty, or diseases. Although there are all kinds of things to get rid of, we usually want to only eradicate the bad things.