"Magic is an inborn talent. It's incredibly rare, and we don't know how or why most people have the ability. It runs in families, pretty strongly - those with a magical parent are almost always magical - but it can crop up at random, too. Nonmagical people are called muggles. Magicals have their own government, that only somewhat interfaces with the muggle government - but, mostly, we work separately and try to remain a secret. The magical government of the Isles considers all magicals born within it citizens, but not muggles - which is why we didn't need your guardians' permission. Acknowledging the parental rights of the parents of muggleborns tends to cause a bit less friction, and the children usually prefer staying on friendly terms with their family, but... The provisions for separating magical children from unsuited guardians are some of our oldest laws, and 'the child prefers it' is considered more than enough."
"Usually we send a representative to the parents of muggleborns - your case was a bit different, since your parents were both magical, and your aunt and uncle are listed as muggles in the know. However, when your letters failed to deliver, the Headmaster of Hogwarts decided to send me to see what was going on."
"Hogwarts operates nine months of the year, and you can stay there the entire time - provisions for the summer are a bit more complicated, since the Headmaster before the current one dismantled the summer residency allowances. Still, there's avenues for you to get dispensation to stay elsewhere, with a suitable magical family - it's easier if you can convince the Headmaster, but we can go over his head to the school board or the Ministry of Magic fairly easily."
"Magicals have our own towns, mostly, with a few neighborhoods hidden in major cities. The neighborhoods in London are the most notable of those, and one of them is usually where students go to get their school supplies. I'll be taking you there - there's an inn we can stay at so you can catch up on sleep."
"For money - Hogwarts tuition is free, due to generous grants from the Ministry and alumni, as well as the combined noble estates of the school's Founders. Needy families can get a stipend for school supplies, but I suspect you won't need one - you should be able to access your parents' bank accounts."
"For magic - wizardry is the art of using a wand to cast spells, pretty much. Hogwarts also teaches some elements of witchcraft, like the use of magical plants and the making of potions."