Let's make it quick, I have the Droid Incredible & looking at my search history on the native browser shows what I look-up on my computer? I use Opera Web Browser on my computer & running 2.1 OS.
Do you mean when you select the "history" link on the Google homepage on your phone? That link displays every google search done from any device that you are logged into google with. So yes, your google searches are constant for your entire account. And it shows what links you click per search. But it won't show links clicked from there on. Google can't follow you that far usually.