Search is somewhat optional, but I guess it got its spot because of Google. It is pretty useful, and I use it all the time, but that's just my behavior.
Menu brings up options for what you can do in an application. For example, in the browser, hitting menu brings up the URL bar and bookmark button (which can also be reached by scrolling to the top of a page), as well as a bottom row of icons with "New window", "Bookmarks", "Windows" (tabs, basically", "Refresh", "Forward", and "More" which contains all the esoteric options for a browser. I guess this could also be put at the top of a browser, but having a handy menu button to bring it up is quite nice for screen real estate. Think of it sort of like hitting alt when you're in a full screen browser to bring up the menu.
What can irritate me about the menu button is that you don't know whether there's anything available unless you press it. It is particularly annoying when you think options should be available and they're not (or they're not where you think they should be).
Honeycomb cleans this up with the action bar. The action bar is on top of the screen and contains whatever actions are currently available. If there are more actions available than what can be fit in the bar, then they get put in a visible overflow menu. The key improvement here is that the action bar is (almost) always visible, so you can quickly glance at it to see what actions are possible (rather than the more complex menu-button flow).
Menu brings up options for what you can do in an application. For example, in the browser, hitting menu brings up the URL bar and bookmark button (which can also be reached by scrolling to the top of a page), as well as a bottom row of icons with "New window", "Bookmarks", "Windows" (tabs, basically", "Refresh", "Forward", and "More" which contains all the esoteric options for a browser. I guess this could also be put at the top of a browser, but having a handy menu button to bring it up is quite nice for screen real estate. Think of it sort of like hitting alt when you're in a full screen browser to bring up the menu.