Presets represent all the values in your entire MIDI Designer setup. For example, a knob called "Sweep" might be set to 45° (or an outgoing MIDI value of 32). When you store a preset, that value is saved. When you recall a preset, all controls snap to the value they had at the time the preset was saved. So your sweep knob would snap to 45° regardless or what position it's in, and that value would be sent out to all hardware/software that is connected.
Presets are available from the main tongue that drops down from "More" for both save and recall. The "alt" button switches to the second group of 10 presets, so you can access 1-10 or (alt) 11-20.
All other editing functionality (including deleting, (re)naming and ordering) can be done via Config -> MIDI -> Edit Presets
Global Presets in 1.5.0
See another question about this here.
Presets for Groups of Controls in 1.6