Perhaps the most prevalent social institution in American society is the institution of marriage.  I would say that marriage performs a few different functions:

• It provides a (hopefully) stable environment for kids to grow up in.
• It helps to socialize the children by giving them an example of how they are supposed to behave when they grow up.
• It allows people to satisfy their sexual urges relatively easily.  It prevents conflict over sexual partners.

A second institution would be the Christian church.  Sociologists would probably say that this functions to

• Allow people to feel more control over their lives.
• Give them hope that their lives have meaning.

Both of these would help keep society stable by making people feel more satisfied with their lives and less likely to cause trouble.