Pretty much what aimvideo says. A cellphone can make/receive calls, sms message, and text messages. They can usually also take pictures.
The line between a cellphone and a smartphone is a bit vague, and moves with the times as features that are unique to smartphones become commonplace in cellphones (such as email).
Generally speaking, having a proper web browser on your phone would make it a smartphone. Things like running 3rd party applications, anything that involves internet access (browsing, email, twitter, facebook, instant messaging etc), and GPS features are all in the realm of a smartphone.