Your new class can be made up of any number and type of other objects, in any combination that you need to achieve the functionality desired in your new class. Because you are composing a new class from existing classes, this concept is called composition (if the composition happens dynamically, it’s usually called aggregation). Composition is often referred to as a “has-a” relationship, as in “A car has an engine.” 
(This UML diagram indicates composition with the filled diamond, which states there is one car. I will typically use a simpler form: just a line, without the diamond, to indicate an association.)
Both Composition and Aggregation are Associations.
Composition HAS-A Association.
Aggregation HAS-A Association.
Composition is a strong association.
Aggregation is a weak association.
Both aggregation and composition are special kinds of associations. Aggregation is used to represent ownership or a whole/part relationship, and composition is used to represent an even stronger form of ownership. With composition, we get coincident lifetime of part with the whole. The composite object has sole responsibility for the disposition of its parts in terms of creation and destruction. In implementation terms, the composite is responsible for memory allocation and deallocation
Moreover, the multiplicity of the aggregate end may not exceed one; i.e., it is unshared. An object may be part of only one composite at a time. If the composite is destroyed, it must either destroy all its parts or else give responsibility for them to some other object. A composite object can be designed with the knowledge that no other object will destroy its parts.
Composition can be used to model by-value aggregation, which is semantically equivalent to an attribute. In fact, composition was originally called aggregation-by-value in an earlier UML draft, with “normal” aggregation being thought of as aggregation-by-reference. The definitions have changed slightly, but the general ideas still apply. The distinction between aggregation and composition is more of a design concept and is not usually relevant during analysis.
Finally, a word of warning on terminology. While UML uses the terms association, aggregation, and composition with specific meanings, some object-oriented authors use one or more of these terms with slightly different interpretations. For example, it is fairly common to see all three UML relationships grouped under a single term, say composition, and then to discuss object-oriented relationships as being either inheritance (generalization) or composition.