"Wait! I forgot an umbrella."
Translation:Чекай! Я забула парасолю.
You use "Чекай" addressing a single person in a friendly manner (you'd use ти when speaking to him or her). For example: Чекай, Томе, ти куди? Wait, Tom, where are you going? (Tom is your friend)
You use "Чекайте" addressing a single person in a formal manner (you'd use ви when speaking to him or her), or when addressing a few people. For example: Чекайте, пане професоре! Wait, professor! (lit. Mr Professor) (you're talking to a professor), or: Чекайте, хлопці! (Wait, guys) - addressing a few people.
Since you're German:
Чекай! = Warte!
Чекайте = Warten Sie! or Wartet!