In general, you will probably do most MIDI editing with the mouse in object mode. This allows you to select notes, copy, move or delete them and alter their properties (see below). But at some point, you're going to want to add notes to a MIDI region using the mouse, and if they are to be anything other than a fixed length, this means dragging with the mouse. Since this would normally be a selection operation if the mouse is in object mode, there needs to be some way for you to tell Ardour that you are trying to draw new notes within a MIDI region. Ardour provides two ways do this. One is to leave the mouse in object mode and Left-drag. The other, useful if you plan to enter a lot of notes for a while, is to switch the mouse into Draw Notes mode, which will now interpret any drags and clicks as requests to add a new note. For obvious reasons, you cannot use Draw Notes mode while using region-level editing.
So, to summarize:
Note that is also a a step entry editor allowing you to enter notes from a virtual keyboard and lots more besides.