What You Need To Know
A secondary mutation is when a mutant develops a new mutation/new power. This mutation could do various things, from giving a new power to returning an old power or building on an old mutation.
Emma Frost - When Genosha was attacked by Cassandra Nova's Sentinels, and they killed most of the mutants living there, Emma Frost's second mutation saved her life. Her new power is the ability to turn her body into near-indestructable diamond, but this power blocks her telepathy.
Black Tom Cassidy - Gained the power of clorokinesis (he turned into and was able to control all plant life). He lost this power when M-Day struck.
Iceman - Iceman's secondary mutation was directly linked to his first: his body was completely turned to ice, and he wasn't able to change back and forth between human and ice form. In this form, if he was destroyed he was basically immortal because he was able to reform himself from water. He lost this power due to M-Day.
Beast - Beast has some sort of secondary mutation, that seems to keep evolving. His beast form evolves into something new.
Angel - Angel recently developed the power to heal others with his blood, providing they're the same blood-type. He may have always had this mutation but didn't realize it, because Icarus, a mutant with similar powers, had healing powers that derived from his wings.
Warpath - Warpath developed the power of self-propelled flight, although for some reason it has never been stated officially that this was a second mutation. This hasn't been exhibited in a while, but he did display some sort of ability to either jump far or fly again recently.
Polaris - After her powers were drained by her alleged half-sister, Zaladane, Polaris developed the ability of super-strength, but she generated negative emotions while doing this. Her powers were later returned and this secondary mutation disappeared.
In Other Media
In the film, Kitty Pryde is shown to have developed additional abilities during the 17 years since X-Men: The Last Stand. While Kitty could initially phase herself and other through solid objects, she is now shown able to send the minds of people back in time into their younger bodies, essentially allowing time travel. This ability proves crucial in stopping the Sentinels from wiping out the entire mutant race.
Additionally, Best is implied to have undergone a secondary mutation in the 10 years since X-Men: First Class. He now sports a more ape-like appearance that looks almost nothing like his previous, cat-like form from the first prequel.