UPDATE – Manual printed I-94 process (mentioned in this old post) has been replaced with Electronic Automated I-94, click to read more.
Just before your flight to United States is about to land, you will be presented a form, by the airline staff, as shown below:
This form is called Form I-94 and it is basically an Arrival-Departure Record of a foreigner, kept and maintained by the US Customs and Border Protection (CBP) and used by USCIS.
You must fill out Form I-94 and present the completed form to customs officer at your respective port of entry (airport) to the United States. The customs officer will stamp the form and keep the Arrival Record portion and returned you the stamped Departure Record portion of Form I-94 (The area highlighted in blue box in above picture).
You must submit the stamped Departure Record portion of Form I-94 when leaving the United States so that your departure can be recorded properly. If you failed to submit the Departure Record portion at the time of departure, it will create a lot of difficulties for you, if you try to re-enter to United States at some point in time in future.