The validity dates of a US visa work differently than in some other countries.
For a US visa, these dates specify the dates which you can arrive at a US port of entry. It does not specify when you must depart.
You can remain beyond the visa expiration date, as long as you remain in status.
For short-term admissions such as tourism and business visits, and for certain work visas, your admittance stamp you receive at the border will show the date you must depart. This is typically six months for short-term admissions, but may be shorter or longer depending on what you told the immigration officer and your visa class.
Public domain image provided by US Embassy Manila
For long-term admissions such as student visas, instead of an expiration date you might see "D/S" which means "duration of status". If D/S appears on your stamp, you need to follow the rules for duration of stay associated with your class of visa (e.g. leaving the US when you are no longer working or studying). In general, when your status ends, you must depart the US.
Image provided by San Francisco State University Office of International Programs