Lecture For All Classes

Charms are a type of magic spell concerned with enchanting an object to behave in a way that isn't normal for that object. For example, the Summoning Charm brings an object to the caster. Charms is also something of a catch-all for spells that aren't Transfiguration (spells that change the inherent nature of an object). In some sense, if a spell isn't Transfiguration, it's probably a Charm.
A Charm might cause something to flash different colors. It might cause an object to levitate or even fly through the air. Charms can make a person laugh or dance or even create a bubble of breathable air around a person's head. In all of these cases, the object or the person doesn't really change, they just do something unexpected.
Some Charms can be extremely powerful. The Fidelius Charm, for example, can completely hide a person or a place in such a way that no one can find them unless they are given the location by a Secret Keeper. Memory Charms can be so strong that they completely remove a person's memory or even damage his or her mind permanently.
Charm spells are in some ways the opposite of Curses: many Charms seem to have an inherent positive tone (e.g. Tickling Charm) while Curses have an inherent negative one. This is not to say that Charms are weaker magic; a well-chosen Charm is a powerful magical tool against curses, jinxes, and hexes.