Advanced magic is characterized by . . .
certain spells that go beyond the capabilities of the average wizard; [these spells] require more than just knowing how to perform magic, but how to master it.
What determines advanced magic?
Apparition – the magical form of teleportation – is not the spell of masters. In fact, it’s a fairly common sight in the world of Harry Potter. But it is a spell that’s notoriously tricky to get right, and particularly bloody if it goes wrong. Hence why, to Apparate and Disapparate, wizards need to be over 17 and have a license from the Department of Magical Transportation, which requires them to pass a test. Similar to Muggles and driving tests, but with slightly more chance of leaving your legs at home. Apparition is so tricky because it requires a high level of mental skill – a level that most wizards, especially kids, are not capable of.
Non-verbal spells are those typically performed with a wand, but without saying the incantation out loud. The advantage, according to Professor Snape, is that ‘those who progress to using magic without shouting incantations gain an element of surprise in their spell-casting. But it’s a feat that requires enormous ‘concentration and mind power’, with the spell-caster having to summon the spell in their mind, rather than out loud. It’s the difference between learning the alphabet, and having to read War and Peace – the students of Hogwarts experience it in their sixth year when they’re expected to perform only non-verbal spells from then on.
Even harder than that, however, is wandless magic. To perform magic without a wand is beyond most wizards. As much as fire, magic can be raging, chaotic and volatile – that’s why wizards use wands to channel it – and requires the utmost skill and discipline to control. Wandless magic is like riding a bike with no hands. During an earthquake.
To cast the Patronus Charm successfully, the wizard casting it must concentrate, with all their might, on the happiest memory they have: it’s fuel for the Patronus, which is a projection of positive energy. To cast either is an achievement, although the latter is so difficult as to be considered unusual. This is because very few wizards possess the skill to concentrate on both the spell and their emotions. Even so, Harry Potter was able to master the spell in his own time at Hogwarts – making him one of the youngest wizards to do so – and he even taught it to members of Dumbledore’s Army, way beyond their years.
All the spells considered advanced magic require concentration of the mind. To apparate you must concentrate on not splinching yourself, to do non-verbal spells you must channel your magic differently, to do wandless magic you must concentrate on controlling your magic, to cast a patronus you must focus on both your emotions and your spell at the same time.
In the end, determining advanced magic is simple. All you will have to do is to see how much mental exertion you use when casting that spell.
All quotes above from the Wizarding World