The verb 呉（く）れる in Japanese, is very similar to 与（あた）える (to bestow). The primary difference is that 呉（く）れる (primarily written in hiragana) means to ‘bestow to the speaker’ (or someone in the speakers inner circle).
In this way, てくれる is the opposite of てあげる, which conveys that someone (usually the speaker) gives (an action) to another person that is outside of their inner circle. てくれる is commonly translated as ‘would you do (A) for me’, as a question, or ‘someone did (A) for me’, as a statement.

• おばあちゃんはいつも美味（おい）しいご飯（はん）を作（つく）ってくれる。
  Grandma always makes delicious food for us!
• 友達（ともだち）が旅行（りょこう）から帰（かえ）ってくるとお土産（みやげ）を持（も）って来（き）てくれる。
  When my friend comes back from vacation, they bring me souvenirs.
• パパ、電気（でんき）を消（け）してくれる？
  Dad, can you turn the lights off for me?

When asking for a favor, てくれる can be shortened to てくれ. However, this is very casual, and should not be used with strangers (or anyone that you do not know well). As an English equivalent, てくれ sounds similar to phrases like ‘would ya do (A)’, or ‘could ya do (A)?’

• お願（ねが）いだから急（いそ）いでくれ。
  I'm begging you, could ya hurry it up?