Any skill or ability that only a select few know how to/can use, from magic to martial arts to metallurgy techniques. Even the art itself
might be unknown to the world at large, but the crux of the trope is that the know-how to use it is limited to a single group or person. Some Secret Arts aren't even particularly jealously guarded and only remain secret through simple obscurity.
Examples are so ubiquitous that I'm having a hard time coming up with straight ones. The Force in Star Wars
can only be used by the very few force-sensitive people, but the know-how isn't entirely
monopolized by the Jedi Order. Alchemists in Fullmetal Alchemist
try to keep their learnings to themselves, but I wouldn't call it a Secret Art
by virtue of its sheer ubiquity and how just about anyone can decide to become an alchemist. Ninjutsu from Naruto
is similar in this regard. Ryu's fighting style (ansatsuken IIRC) in Street Fighter
isn't very plot-relevant I guess, but I think it's the most straightforward example, being a martial art taught by a single master.