Brutalities are brutal, oftentimes fatal finishing moves that require specific conditions and combos to trigger. Usually, these are triggered when the victim's HP is in critical levels. In MKX, there are certain brutalities that are available only on certain variations. Most brutalities are locked per character, and you need to spend Koins in the Krypt to unlock more of them. They're the hardest to pull off and sometimes can be more satisfying that Fatalities.
Also, there are Stage Brutalities that can be triggered by using objectives that you can interact with on stages. For example, in the stage Outworld Marketplace, you can throw the old lady to a low HP opponent and cause him/her to explode extravagantly. (There's also an associated trophy for this)
Another example is in Dead Woods, where you can use a branch that you can break to impale your critically wounded opponent. Unlocking a hidden Stage Brutality for the first time will earn you 20,000 Koins that you can use to spend in the Krypt.