Player can or must occasionally holster, sheathe or otherwise lower their weapons or drop a combat stance to avoid unnecessary fighting. Usually to avoid intimidating allies, neutrals, or bringing the ire of any law enforcers.
Alternate names: Sheathing, Lowering weapons, Weapon concealment
The first video game about Holstering was released on August 31, 1996.
* Stealth - weapons may make you more visible, often due to metal they're made out of.
Nor is this for cases where it makes running easier/faster. In reality, sheathing a sword should not make running any easier than holding it in your hand, but maintaining a combat stance or readiness to strike while running would seriously impair running. Especially notable with polearms, which in reality you can't sheathe or put away other than dropping, and even if you could, it likely would make running harder than holding it in your hands. In cases where this does make it easier, one can usually assume the change is from combat stance to casually holding the weapon (even if the graphics suggest otherwise).
Generally speaking, guards, police, etc. might get mighty interested in interfering with your business if you run about brandishing a weapon. Civilians might run away from you, call for the police, and so forth.
Note on naming:
There's apparently no generic word for "lowering/hiding your weapons and/or combat stance" we're stuck with something that implies firearms. However, this is for all kinds of weapons (guns, swords, crossbows, stilettos, wooden pegs, etc.) and combat stances which suggest you're ready to beat the crap out of people.
This also includes hiding your weapon in stealth games as it's assumed to be the same as holstering/sheathing.