To forsake another person is to leave them entirely, usually in a moment of need.
Forsake may mean simply giving something up, such as a way of life or a homeland, for something better or more appropriate. But it is often a mean word, suggesting leaving something or someone behind when they need you to stay. One way to remember the meaning of this verb — to abandon or desert — is to remember this little sentence: "For heaven's sake, don't leave me, or heaven is lost!" Lose the heaven, and you have forsake.