spells - Why did Witches and Wizards in Harry Potter need wands to perform magic well?

It always bothered me that they needed the wands to do magic. In the first film/book, before Harry went to Hogwarts, there were instances of him using magic unintentionally without the use of a wand (such as turning his teacher's wig blue).

Why do they need them? Are there any that don't need them to intentionally use magic, if so, why?

Clarification edit: I mean are there any that are able to do magic well without the use of a wand?

Answer

Witches and Wizards use wands to help channel magic.

I would imagine that European wizards like Harry who are used to always having a wand when performing magic, would find it difficult to do so otherwise. However, in some other of the globe, wands are rarely, if ever, used.

The wand is a European invention, and while African witches and wizards have adopted it as a useful tool in the last century, many spells are cast simply by pointing the finger or through hand gestures.

_{(Pottermore - Uagadou)}

Some wizards are able to do magic well without the use of a wand

The magic wand originated in Europe. Wands channel magic so as to make its effects both more precise and more powerful, although it is generally held to be a mark of the very greatest witches and wizards that they have also been able to produce wandless magic of a very high quality. As the Native American Animagi and potion-makers demonstrated, wandless magic can attain great complexity, but Charms and Transfiguration are very difficult without one.
_{(Pottermore - History of Magic in North America)}