Real Robots are usually designed and manufactured by the military or by corporations, as opposed to the Mad Scientists/nutty professors who crank out Super Robots. In addition, while Super Robots are usually piloted by the professor's nephew or some other Boy of Destiny, the pilots of Real Robots tend to be military personnel or mercenaries contracted out from some wing of the military/industrial complex. While many Super Robots can be repaired with Hot Blood or The Power of Friendship (or simply never take serious damage at all), repairs on Real Robots tend to be a time consuming and costly affair.
While a Real Robot pilot may have special powers, they don't require them to pilot the mecha, unless the mecha makes use of very special equipment — and even then, in nearly all cases, the mech can be piloted by somebody else with the same ability, or even without that ability, who will simply be unable to use the special equipment. Real Robot series tend towards the themes of "War Is Hell" or "We're all alike, if only we could sit down and talk to one another".
Real Robots are very often damaged, even destroyed during the series, and in many cases, main characters get killed in rather pointless ways... just like in a real war. A Real Robot doesn't require being made with current technology, but does require a relatively well-tested, "hard science" aspect at its core — something with properties which are very well defined in scope and limitations.
Real Robot series tend more towards "cynicism" on the Sliding Scale of Idealism Versus Cynicism. If they're computer games, they tend to opt toward more "realistic" controls using as much extra input hardware as they can get their players to buy, sometimes even making their own. Alternately, they can be incorporated into wargames, with the player giving orders to a squad of mecha.
The distinguishing trait between Real Robots and Super Robots is whether the mech is seen as a tool or a vehicle: a Super Robot acts like a tool, in that its a focal point for the pilot, who supplies the skill, willpower and sometimes power; a Real Robot in contrast acts like a vehicle, it has greater power, speed, mobility or defense than the pilot, who serves as the equivalent of higher brain functions.
The expression originally came from "Real Robot Line", a term used by Sunrise in the 80s to promote their Gundam and Gundam-like animes during the decade. It became popularized in the West thanks to Super Robot Wars using Real Robot and Super Robot in an attempt to distinguish Mazinger Z and Mobile Suit Gundam units. Super Robot Wars OG series later define their original mechas that Super Robots are designed for a specified reason and are usually ready to fight against many opponents while Real Robots are designed to excel in common situations and in groups.
Aside from Gundam, other famous franchises that were in the Real Robot Genre were the Transformers franchise, as well as Macross, Machine Robo, and Robotech franchises.