Expanding is basically enlarging your base to close or remote locations. Expanding can be used to secure Ore Nodes, Tech Structures, or to set up a forward base. It is common to expand your MCV, build some structures, and then pack up and move somewhere else. All units that are used to expand have no weapons and must be protected from enemy attacks.
The Allies can expand with their Prospectors. The Prospector deploys into the Command Hub, which gives a larger amount of ground control than the Soviet Sputnik, but takes more time to deploy. However, each Command Hub must be teched up individually.
The Soviets expand with their amphibious Sputnik vehicles. They unpack into Outposts, which give less ground control than Command Hubs, but unpack much more quickly.
Nanocores — The Empire has the easiest way of expanding thanks to their Nanocores, which can deploy almost anywhere on the battlefield. Nanocores are excellent for taking Ore Nodes. It can be a good idea to have a contingent force of Nanocores on standby to set up a forward base, or to set up another base, in case your original one is destroyed. All Structure Nanocores, however, have a small ground control around them once deployed, which makes enclosing your base with walls hard. Furthermore, each factory building has to be teched up individually, which hinders you from pulling out high tech units from front line factories too easily.