Because the ranking system of Google ranks sites partially by the number of other sites which link to them, a group of determined people can push up a particular site's ranking when a specific word is searched by creating lots of pages which link to that site.

The first organized Google Bombing campaign is said to have been started as a joke by Adam Mathes an "internet celebrity". He discovered that you can bump up a pages ranking by making lots of links with a particular phrase in the link phrase, and used this technique to bump up the link of a "friend", Andy Pressman. He did this by linking lots of pages to Mr. Pressman with the phrase Talentless Hack; for a while, a google search of the words "Talentless Hack" came up with the hapless Mr. Pressman's web page.

I suppose it makes sense, in a sad kind of way, that the first Google Bombing that made national news was performed by the antisemitic web page JewWatch. By getting larval antisemities to link to Jew Watch incorporating the word "Jew" into the link phrase, Jew Watch became the number one result to the query Jew. At that point, two things happened: Determined Jews created a countercampaign to Google Bomb wikipedia's entry on Jew, and knock JewWatch out of first place, and Google took out an ad on their own web page to both apologize for the results and claim that there was nothing they could do about it. Currently Jew Watch and the Wikipedia entry vie for first place as Jews (and those who admire them) and their antisemitic antagonists fight - through linking - for the upper hand.

The best explanation of how to Google Bomb is on Adam Mathes web page: