Most people would use MIDI to quantize drums that may sound a little off beat. This can be simply done by any DAW since MIDI is simply digital information which triggers sounds. However if you want to play drums from an external source e.g. drums on a synthesizer, those sounds would normally be interpreted as Audio, not MIDI.
See below for the Audio file created by me playing the drums through my keyboard as Audio.
As you can see, the beats are not perfectly aligned with the grid and many sound slightly off beat. Now if you right click and select Quantize the audio part (the attack) will be snapped onto the grid as per below.
As you can see from the above, the beat are now aligned with the grid. This is probably better for the electro side of music but not for the Neo Soul or live drums. Too much quantization can leave it feeling very stiff and unnatural sounding. Incidentally you can move the beat positions around by dragging the yellow arrows indicated at the top. The grid width or quantize amount can normally be adjusted.
Funky quantization can be achieved be setting the grid into Triples as opposed to whole beats.
Also remember you have the “Swing” function on most DAWs which gives more of a human feel to beats or rhythms.