This page of the Doom Eternal guide explains how to use the grappling hook. This gadget is able to pull yourself towards opponents and damage them with a melee attack.
The grappling hook is only available for the Super Shotgun. You get this weapon during mission 3 - Cultist Base.
You shoot the hook by holding down the weapon's alternative attack button - on consoles, it is left trigger. This action will only work if you have a demon in your crosshair that you can grab. You also need to be within the grappling hook's range.
You pull yourself towards monsters for two reasons:
- You can fire the Super Shotgun from a very short distance.
- You can use a charged Blood Punch. If the Blood Punch is strong enough, the monster will die instantly.
Using the grappling hook is optional for the vast majority of the campaign. The exception is the penultimate boss - Khan Maykr from mission 12. Every time you destroy her shield, you have to pull yourself towards the boss and use Blood Punch to take 1 health point. You will have to do it a few times.
For more information, check out the strategy for Khan Maykr featured in the Bosses chapter.