Visa expiration date and the authorized period of stay are both two different things. If you are a citizen of a foreign country, to travel to the U.S. temporarily you must obtain a non-immigrant U.S. visa. You need to get a visa from a U.S. embassy or a consulate in your home country. That visa will be attached to your passport. There are different types of visas and depending on the purpose of your trip you will need to apply for and get the right type of visa.
With a visa, you can travel to a U.S. port of entry and getting a visa does not mean that you will be granted entry into the country. Your passport and other documents will be reviewed by immigration officers at the port of entry. You will be granted entry only after the immigration authorities determine that you are eligible to enter into the U.S.
Visa validity date will be indicated on your visa and you can enter into the U.S. with that visa as long as it is valid. With a single entry visa, you can travel to the U.S. only once and with a multiple entry visa, you can travel to America more than once. Multiple entry visas can be used to travel to the U.S. more than once, but you can travel to the U.S. only for the purpose for which it was initially issued.
The visa validity date and the authorized length of your stay in the U.S. are both different. If you hold a multiple entry visa and if that visa is valid for ten years, it does not mean that you can remain in the U.S. for ten years. Form I-94, Arrival/Departure Record, that registers arrivals and departures of non-immigrants will be issued to you by the U.S. Customs and Border Protection officers at the port of entry. After determining that you are eligible to enter into the U.S. they will indicate the date on which you will need to leave the U.S. on Form I-94.
You can legally stay in the U.S. till the date indicated on Form I-94. In case you need to stay in America for few more days, you must apply for an extension of stay by filing Form I-539, Application To Extend/Change Non-immigrant Status. You need to file an application to extend your stay before your non-immigrant status expires. If you fall out of status, you will not be able to remain in the U.S. and you will be subject to deportation.
For information on visa processing times, USCIS service center processing times, USCIS local office processing times and expected border wait times, please visit http://uscisprocessingtimes.org/