Physically quantizing notes changes the actual start time and duration of the notes, affecting how they sound as well as how they are displayed. When notes are quantized to a certain value, the start time for the note is a multiple of the quantization value and the duration of the note is a multiple of the quantization value. Quantizing the selected notes to 64th means that the start time and durations of the notes will be multiples of 64ths.
Select the note or notes you want to physically quantize by double clicking, control-clicking or dragging over them. From the Edit menu choose Quantize. A submenu will appear to the right of the menu, showing all the quantization options. The checked quantization value is the current display quantization. (This can be changed using the Display menu.)