The Refusians once had a physical form, but a giant solar flare caused them to lose their bodies and, as a result, they no longer had a recognisable "being". The Refusians were not only invisible to other races, they were also invisible to one another; they could only sense another Refusian's presence.
In their new forms, the Refusians were super-strong and could move heavy objects — such as the giant Monoid statue containing Monoid One's fission bomb aboard the Ark, for example — as if they were practically nothing. They were also an advanced race, possessing various weapons that seemed to have a wide range of capabilities, from stunning Monoids to blowing up landers, without even being seen to operate.
Despite their newfound talents, the Refusians missed seeing signs of life on their planet. Once they became aware of the Ark's journey to Refusis II, they welcomed it and began constructing a city in which the humans and Monoids could live. They were dismayed to see the fighting between and among the groups when they arrived on Refusis and agreed to help the First Doctor defuse the situation. Once the humans had been saved from destruction, and the Monoids had quit fighting, the Refusians ordered them to begin living together in peace if they wanted to stay on the planet successfully. (TV: The Ark)
Shortly after the TARDIS departed from the Ark, the Doctor suddenly turned temporarily invisible, as well as intangible, with Dodo Chaplet and Steven Taylor thinking this was caused by contact with the Refusians. In reality, it was a trick done by the Celestial Toymaker. (TV: The Ark, The Celestial Toymaker)