The ~てくれる form expresses that someone does something for the benefit of the speaker (or the speaker's in-group). It highlights the speaker's gratitude or appreciation for the action performed by someone else. The subject of the verb is the person doing the favor, and the recipient (often the speaker) is marked with に, though it is frequently omitted when context makes it clear.
When someone performs an action that benefits you, use ~てくれる to acknowledge that kindness.
The nuance of ~てくれる is that the speaker feels thankful or views the action as a favor. Without くれる, the sentence would simply state a fact without conveying this feeling of gratitude.
Compare:
In casual speech, ~てくれる? is used to ask someone to do something for you. It is a direct but informal way of making a request.
The negative form ~てくれない? is also used for requests and can sound slightly softer or more indirect.
The polite/honorific equivalent of ~てくれる is ~てくださる. It is used when the person doing the favor is someone of higher status or when you want to show more respect.
The polite request form ~てください (please do ~) is actually derived from ~てくださる.
Both ~てくれる and ~てもらう express receiving a favor, but they differ in perspective:
Compare: かれ彼にえき駅までおくって送ってもらった。 – I had him drive me to the station.