Quantize lets you tighten up the rhythmic feel of your music by aligning the notes to a “Time Grid”. There are two main types of quantization available to you: Notation based and custom.
Notation based quantize uses the same process used to display your music in the Notation view. You can think of the Notation based quantize grid as being “flexible” in that it will bend and stretch to try to make musical sense of your selection. It can accommodate notes on even beat divisions as well as triplet divisions in one pass. In essence, what you see in the Notation view is exactly how the music will be quantized, except Notation based quantize does not change note durations.
Custom quantize, on the other hand, uses a fixed grid, but gives you complete control over it.
Notation based quantize is great when your playing is fairly exact, but you just want to tighten up the overall feel. Use custom quantize in situations where you want to alter or precisely control the rhythmic feel.