The slope selection is whether you want to trigger on the rising edge of falling edge of the waveform.
AC/DC selection is whether you want to trigger on a fixed DC level of the waveform or just the AC part of the waveform independent of its DC level.
Video trigger is optimized to allow stable triggering with composite video waveforms (particularly old NTSC or PAL video signals) which include the sync signal. It likely has a sync separator circuit to allow triggering only on the sync.