A warp-capable civilization or warp-capable species was any spacefaring civilization that was technologically advanced enough to develop ships that were capable of spaceflight at warp speed.
The United Federation of Planets considered such cultures acceptable to make first contact with. Any culture that hadn't yet developed the technology, was a pre-warp civilization and as such was protected by the Prime Directive, also known as General Order 1, which forbade contact, as there was a danger of cultural contamination. (TOS: "Bread and Circuses")
To the Borg, the species they designated Species 5618 – known colloquially as Human – was described as being "warp capable." (VOY: "Dark Frontier")
T'Pol explained to Jonathan Archer that, in the time Vulcans first went into deep space, there were fewer warp-capable species and thus fewer hostile aliens. (ENT: "Silent Enemy")
Prior to the Valakians' first contact with Humans in 2151, Valakis was visited by two warp-capable species, the M'klexa and the Ferengi. (ENT: "Dear Doctor")
In 2370, the Hekaran scientist Serova opened a subspace rift by overloading her ships engines to a warp core breach in the Hekaran sector, demonstrating that conventional warp engines did in fact cause severe damage to the fabric of spacetime. In order to slow the rate of the damage, the Federation shared all the data with warp-capable species and imposed a speed restriction of warp factor 5 on all Federation vessels in all but extreme emergencies. The areas of space most damaged by that point were restricted to essential travel only. The Klingons were expected to follow the restrictions, but Deanna Troi and Worf thought it unlikely that the Romulans, the Ferengi and the Cardassians would. (TNG: "Force of Nature")