Non-verbal spells are spells executed without the caster pronouncing their incantation out loud. Not all wizards possess this skill. According to Hermione Granger (quoting almost word-for-word The Standard Book of Spells, Grade 6) the advantage of this sort of spellwork is that "Your adversary has no warning about what kind of magic you're about to perform, which gives you a split-second advantage."
Severus Snape teaches non-verbal spells to his sixth-year Defence Against the Dark Arts class; it is the first subject of the year. Most students have difficulty grasping the skill, especially Harry Potter (HBP9). Later that year, the boy performs Levicorpus without difficulty (HBP12).
Other uses of non-verbal spells in canon include: