Classes can be compared to technical designs of machines, objects to machines... from one technical design, many machines can be created.
This is simplification, for objects can also represent beings, qualities, or even different ideas from ones mentioned just before.
That is, objects can be symbols (symbols represent ideas) in a play of ideas, with a computer program being a plan for such a play, a process - a running program: this play in action with side effects, and computer system: a container for such a play.
Class is abstract data type with full or partial implementation. Classes form a static structure of a program.
Object is instance of a class during a runtime. Objects form runtime structures.
Objects together can collaborate, communicate, and model a system.
Source: , perhaps more.
See also, if You wish: Type, State, Context, Object & Class.