Cybermites were cybernetic insects, controlled and created by the Cybermen. According to the Doctor, they were a heavily upgraded form of Cybermat. Even one could partially convert people, but to have a full upgrade would take a very large swarm. Because of this, they usually travelled in small swarms, and went directly for the victim's head. They were not used in the upgrade process for a full cyber-conversion.
The partial cyber-conversion was accomplished by the cybermites grafting technology and cybernetic implants directly onto the victim's skin. When they converted Webley, the right side of his face and his right hand were completely cybernetic. However, Angie and Artie only had a small implant on the left side of their face that induced a trance state, similar to the earpods used by the Cybermen from Pete's World. When the cybermites converted the Doctor, an implant covered the left side of his face but resulted in the creation of a Cyberplanner with a manic personality, "Mr Clever".
Thanks to their small size, the cybermites were perfect for spying on others and were thus used by Cybermen for reconnaissance and intelligence gathering. Their "eyes" were capable of scanning environments and individuals and the data was transmitted back to the Cybermen.
A small Cybermite horde could restore and enhance some functionality of a broken, obsolete Cyberman shell, but not completely reconstitute one. They would use it as a nest, waiting until a susceptible target for conversion came near. Then, the Cybermites would puppeteer the Cyberman husk to restrain them, and scurry out of the casing for the act of converting the captive. (TV: Nightmare in Silver)
After Hedgewick's World of Wonders was destroyed with the three million Cybermen on it, it was assumed the last of the Cybermen were destroyed. However, a single Cybermite survived, drifting in space, allowing the Cybermen to be revived. (TV: Nightmare in Silver, WC: Who Are The Cybermen?)