The branch of the military denoted by the word Signals is, essentially, that of communications, though often also encompassing elements of Intelligence in the form of SIGINT (Signals Intelligence). Historically, the name derives from the practice of using signals - flags, lamps, and so on - which use eventually led both to the formation of separate specialist occupations (Signaller or Signalman) and military organizations (Signal Corps). In modern times, however, many have come to prefer the term "military communications" to describe the purpose and objectives of the various national signal corps, as with the advancement of technology the domains in which a signalman might find him- or herself have broadened significantly. In Canada, for instance, the trade of Signal Operator, or SigOp, is undergoing an amalgamation with the related trades of Linesman and LCIS (Land Communication and Information Systems) Technician; while the SigOp is technically a radio operator, the Linesman technically a wired-communications operator, and the LCIS technically a networking-and-computer-maintenance technician, the digitization of communications technology has rendered the distinctions blurry (except, of course, to those in the given trades; for instance, SigOps exemplify the motivated problem-solver, while Linesmen are lazy but hard-working when they have to.*)
While often overlooked in the face of the more glamourous combat arms branches of the military, Signals still plays a vital role in command and control, being the intermediary between squad, unit, and army-level communications. For example, while a unit's individual radios may continue to work in the absence or destruction of a comms truck, they will have no way to communicate nor to receive orders and information from the chain of command. Furthermore, Signals plays an important role in the gathering of military intelligence, as not only intercepted communications, but also use of passive sensors (considered part of ELINT, or Electronic Signals Intelligence, one of the divisions of SIGINT) can prove invaluable in determining enemy strength, position, and movements. Of course, this is a double-edged sword; a comms unit not taking proper precautions will soon find itself targeted by an informed enemy aware of its importance.
* For bonus points, guess the noder's occupational specialty!