Cellular refers to the structure of the network that phone uses. With cellular phone being the North American term for a mobile phone.
Cellular networks are broken up into cells, these cells are defined by base stations and the distance to which they propagate coverage. In them, radio waves are used instead of physical connections to transmit incoming and outgoing signals. Each base station is allocated a band within the Ultra High Frequency (UHF) portion of the radio frequency spectrum. Adjacent cells must not use the same transmission frequencies, as their areas of propagation overlap, and would cause interference. However, Non-adjacent cells are far enough away for their to be no overlap and frequency re-use is feasible.
Each base station has a limited number of uplink and downlink frequencies, to allocate to phones connecting to the network (making a call). However, because only a comparatively small amount of people are ever connected to a call at any one time, this limit is rarely every reached. An example of when an instance of this has occurred would 7/7 London Bombings, where a large part of the O2 network in London was shut down to everyone (excluding members of emergency services), so as to prevent the system from overloading and crashing calls.
For the 2012 London Olympics, pre-emptive measures were taken to ensure that the network could accommodate the increased number of uses that would be using it. Additional base stations were set-up temporarily around the area at which the Olympic grounds were.