subpixel motion is when an object is animated such that it shifts in non-integeral distances, such as moving and edge X.5 pixels down, etc.
kinda like....AA but animated in a way, in that AA is showing when an edge is half-on half-off a pixelwidth....and subpixel movement is such that a frame shows it half-on half-off a pixellwidth. even at it's simplest it is different than cut-and-paste in that you are required to redraw at least the edges of colors in order for it to be subpixel.
Actually it can be done using copy + paste -- you select the area that you want to move, plus some bordering (if you're moving it 0.5 pixels down, you need to select with an extra row on the top; if you're moving it 0.5 pixels left, you need to select with an extra column on the left, ...); Then you copy it, paste it; Round the offset up to the nearest integer and move it that number of pixels (eg. if the x,y offsets were 0.25,0.25 you move it +1,+1 pixels); then you set the opacity to match the offset (eg. 25% opacity to match 0.25 offset)) and merge the pasted layer with the underlying sprite.
in short: copy, paste, move, set opacity, merge. (and reindexize it to the previous palette)
That doesn't handle masking/transparency in a sprite-ish way, so you would have to touch up some edges if you needed to offset a partially-transparent bit. unless you had alpha channel in your sprites, in which case it would be perfectly correct and excellent.
That method is always perfectly uniform, so it's usually a good guideline.
Using paintprogram rotation to get subpixel rotation and combining that with the above technique is also good for working out guides.
to be honest i always thought it was the same as redrawing AA on each frame for the longest time.
I think it's easier if you have the frames without AA and then render them all at once.
Then it works to just 'push around' the AA for any minor movement effects.