In Deathloop, Colt has to kill his enemies and do so quickly. He's got just one day to take out the 8 Visionaries stationed on Blackreef. While running in guns blazing is an option, stealth affords a level of nuance that lets Colt end a fight before it even starts, and executions are an excellent tool of the trade.
To execute enemies, sneak up behind them without being noticed. Wait for an R1 prompt to appear on the screen with a skull next to it. This icon indicates that Colt can execute an enemy. Press R1 after this icon is on the screen to instantly dispose of an enemy.
Meleeing enemies is an effective way to deal with single targets in Deathloop, and playing stealthily will allow Colt more opportunities for executions. It's a handy mechanic that helps pick off the opposition quickly and quietly.
Pairing executions with abilities and weaponry will be integral to Colt's success on Blackreef, so make sure to pair this ability with the other tools and tricks at Colt's disposal.
For more on Deathloop, check out some of the other guides here on Pro Game Guides, like How to play Multiplayer in Deathloop – How to play as Julianna the Assassin or How to unlock and change outfits in Deathloop.