DHCP allows us to re-use IP addresses so we do not need one for every device. IP addresses are loaned out to devices for a limited time. Much like a library book, devices can continue to renew the IP addresses as long as they need them.
Since we have a large number of mobile devices on campus, our lease times for IP addresses are set at 15 minutes. At half of that interval, the device will usually ask to renew the IP instead of waiting until near the end of the lease. After 15 minutes without a renewal, the IP address is given up and put back in the available pool.
For more information, the Wikipedia article will give all the gory details.