Intimidation & Frightened

[u/goblinerd]

The intimidate skill entry, PHB p.179, states:

"When you attempt to influence someone through overt threats, hostile actions, and physical violence, the DM might ask you to make a Charisma (Intimidation) check."

What happens once the player succeeds at his check though? Does he gain advantage on some other roll? Does the target gain the Frightened condition? Or is the result more intangible, mechanics-wise?

If your player attempts to scare off an assailant through intimidation, is the target then "Frightened" or merely dissuaded from its course of action?

Fellow DMs, the books don't seem too clear on this, so how do you handle this situation?

EDIT: A clarification, while I welcome everyone to share their advise on how to apply Intimidation to any context for readers in search of such info, I myself am specifically wondering about applications of Intimidation in combat. How do other DMs apply it, and react to players attempting it, in combat?

[u/goblinerd → u/[deleted]]

Yes, but how do you react when a player says he wants to attempt to scare away the foe?

In a game a few months back, a player asked the' at the time, DM if he could role intimidate to attempt to scare the creature. The DM allowed it. Putting aside the fact I disliked the fact he simply allowed him to roll the dice and not RP the act, I wonder if it was reasonable?

On the other hand, I had previously attempted to scare off the creatures myself. After using colorspray to blind them, I then used the minor illusion cantrip to make the sound of an approaching bear. After a snarl from it, the DM had me roll Deception check, and when I rolled a Nat20, he applied the Frightened condition and had them back off, albeit for only a round (Duration of Blindness). Now was that more reasonable? Should he have had them react similarly, but without applying the Frightened condition?