The rectangle is the UML icon for representing a class. The name, attributes, operations, and responsibilities of the class fit into areas within the rectangle. You can use a stereotype to organize lists of attributes and operations. You elide a class by showing just a subset of its attributes and operations. This makes a class diagram less busy.
You can show an attribute's type and an initial value, and you can show the values an operation works on and their types as well. For an operation, this additional information is called the signature.
To reduce the ambiguity in a class description, you can add constraints. The UML also allows you to say more about a class by attaching notes to the rectangle that represents it.
Classes represent the vocabulary of an area of knowledge. Conversations with a client or an expert in that area reveal nouns that can become classes in a model and verbs that can become operations. You can use a class diagram as a way of stimulating the client to talk more about his or her area and reveal additional knowledge.