At the time of your arrival in the U.S., you will be required to produce your passport and to surrender your certificate of eligibility (Form I-20 or DS-2019). The immigration officer will issue an arrival/departure record (Form I-94). Your date and place of entry and visa status will be indicated on these documents. The immigration officer will also determine your authorized length of stay.
If on an F-1 or J-1 visa, your I-94 will be stamped D/S (Duration of Stay). Generally, this means that you may remain in the U.S. for the length of time that it is expected to take you to complete your degree plus 60 days. If on an F-1 visa, you will receive page 3-4 of your I-20. If on a J-1 visa, you will receive the pink copy of your DS-2019.
All of these documents should be kept in a safe place. They contain important immigration information and are necessary for identification, school registration, and future travel outside U.S.