We all know most spells' names are shouted out loud when casting in Harry Potter. Some spells are exception. Two I can think of are Apparition and just before Sectumsempra HP cast on Draco Malfoy in HBP (I don't know the spell's name, but Potter and Malfoy were shooting at each other). Why is this?
Reference to NonVerbal Spell
Severus Snape: "What is the advantage of a nonverbal spell?"
Hermione Granger: "Your adversary has no warning about what kind of magic you are about to perform, which gives you a split-second advantage."
— A sixth year Defence Against the Dark Arts lesson
A nonverbal spell is a spell which is performed without saying the incantation out loud.
Hogwarts School of Witchcraft and Wizardry begins teaching nonverbal magic to students in their sixth year in Defence Against the Dark Arts, Charms, and Transfiguration; the students are expected to use spells nonverbally from then on.
Harry used some nonverbal spells :
Levicorpus : Though Harry found nonverbal magic very difficult to do, he was eventually able to cast this spell, which is meant for nonverbal use, nonverbally.
Liberacorpus : Harry used this spell nonverbally to counter act the Levicorpus spell he used on Ron Weasley in 1996.
Harry Potter attempted to use the "Summoning Charm" nonverbally and "wandlessly" to retrieve his fallen wand when he was paralysed by Draco Malfoy, but to no avail.
Harry Potter performed nonverbal magic when he cast his "Patronus" during the Battle of Hogwarts.
In the Harry Potter universe, some wizards are able to cast "non-verbal magic" - in other words, they can perform spells without saying the name out loud. I don't know whether Apparition falls under this category, but the second example (Harry and Draco shooting non-verbal curses at each other) definitely counts. Another example would be the duel between Dumbledore and Voldemort in Order of the Phoenix.
Use of non-verbal magic is more prominent in the films than the books, presumably for dramatic purposes - if everyone called their attacks all the time, it would interrupt the flow of the battles and slow down the pacing. Compare the non-verbal duels to, for example, your average Sailor Moon fight.