fill_parent

Setting the layout of a widget to fill_parent will force it to expand to take up as much space as is available within the layout element it's been placed in. It's roughly equivalent of setting the dockstyle of a Windows Form Control to Fill.

Setting a top level layout or control to fill_parent will force it to take up the whole screen.

wrap_content

Setting a View's size to wrap_content will force it to expand only far enough to contain the values (or child controls) it contains. For controls -- like text boxes (TextView) or images (ImageView) -- this will wrap the text or image being shown. For layout elements it will resize the layout to fit the controls / layouts added as its children.

It's roughly the equivalent of setting a Windows Form Control's Autosize property to True.