てください is a polite expression that is used for asking people to do something. It is most often translated as ‘please do (A)’.

• 手（て）を洗（あら）ってください。
  Please wash your hands.
• これを見（み）てください。
  Please look at this.

ください is actually classified as 尊敬語（そんけいご）, a type of polite speech that is used to refer to the actions of other people. くださる itself is the base form of this verb. While ください is exclusively used for making requests. くださる is the polite (sonkeigo) equivalent of くれる.
In friendly conversation, ください can be omitted from this expression, and the て form itself can be used as a very casual way of saying ‘please do (A)’.

• ちょっとテレビを消（け）して。
  Hey, can you turn off the TV? (ちょっと is often used simply to get the attention of the listener)
• クッキーを作（つく）ったから食（た）べて。
  Because I made cookies, you can eat them.