The refill glitch is the trick that overlaps the refill cutscene that plays when morphing into a statue's hands, and the new item cutscene that plays when you pick up the new item that was in the statue's hands. This trick involves opening the item and morphing into the hands before the item's hitbox becomes reachable, and there is a very small window to do this. Most statues are set up in a way where you can perform a series of inputs similar to a Jump Bomb Jump, except instead of timing the second jump to get pushed by the bomb's explosion you instead time it slightly later so you land right right as its exploding but after the point where it would have propelled you up.
It is also possible to stand on top of the item shell, jump straight up, and time a shot so that you open the item and immediately morph into the hand to get the refill glitch, though I don't have any footage at this time to show what that looks like.
The time saved from the refill glitch is not a significant amount of time, so any time spent setting up for the trick instead of just immediately going for it will likely already lose you any time you would have saved if you had just collected the item normally. If you attempt the refill glitch and miss it, just grab the item so you don't lose more time by this point.
Some statues in the game have springball setups which are much easier versions of this trick. They generally involve holding the A button and entire time and timing the bomb with a visual cue. Here are some of the more common springball refill setups:
Any% - Ridley's Unknown Item with the Early Hi Jump route
Morph onto the floor, roll up to the statue, and press and hold A and B at almost the same time. You need to press B just a few frames after A so that the bomb is a little off the ground when it explodes for the timing to work.
Any% - Speedbooster
You should already be morphed entering this room because you need to bomb the blocks to leave Kraid's room. While rolling into the room, hold A at the point where you would reach the statue with your jump. Press B to lay a bomb near the lower half of the statue's hands. Continue holding A the entire time and the timing should line it up perfectly every time.
100% - Screw Attack
If you're doing the Newfair route and you're not comfortable with your health for the upcoming hellrun, refilling at Screw Attack is your best bet to survive the trip. This setup involves rolling into that gap between the door and the statue and holding A as you're falling into the gap. Continue holding A the entire time, and press B to lay a bomb just at the lower half of the statue's hand. It is also possible to do this one without falling into the gap, but you would need to manually aim your first jump to land right in front of the statue hands.