Rolling into a damage source whilst shielding and holding down results in what's called a weirdslide, wherein Link shuffles his feet awkwardly and moves around sporadically. During this animation there are frames where it's possible to detach the camera from Link's model by using a first person item, like the slingshot or hookshot. This is basically what's happening during a weirdshot.
Using the hookshot, this is very useful glitch since with the use of a single bomb we can go around walls by detaching the model below the ground and hookshotting onto walls, chests, and sometimes enemies in order to skip large sections of gameplay.
Weirdshots are quite difficult to execute due to the large concentration of inputs and the small amount of frame windows, but there are many setups. One of the first was made by Sockfolder and is detailed in the following video.
This setup is very difficult to do unbuffered and is therefore not used much these days, but it's a good starting point.
What's happening is that you shield drop a bomb on a particular frame of a backflip so that the spacing between you and the bomb is proper to initiate a weirdslide. An easier setup that abuses a similar mechanic is given by Enu. In this setup, we bonk against a wall so that when we drop a bomb and roll, then backflip, the spacing is similar to the above setup.
Both of the previous setups rely on abusing spacing so that getting a weirdslide is automatic. However, it is possible to manually initiate a weirdslide by holding down on the same frame you shield an explosion after rolling. Getting this down takes practice, but if you can perfect it, freestanding weirdshots are a close next step. It's rare that you'll ever have to do a weirdshot without a wall nearby, but other factors could contribute so that there isn't enough room for Enu's setup. These kind of "freestyle" weirdshots are shown off by Zas in this video.
Weirdshots are incredibly useful in certain areas such as obtaining the Fire Temple Boss Key without getting the hammer, obtaining Ice Arrows or chus from the Gerudo Training Grounds without going through them, and going through the child side of Spirit Temple as adult with the Longshot.