I'll start by saying, having used a few other programming languages, the concept of an object in Objective-C is pretty much the same as it is in other Object Oriented Programming languages. There's a good writeup on Wikipedia.
I'd say an easy way to think about it is that a "class" is a blueprint. It describes how a thing should work. An "object" is an actual instance of a thing that follows that blueprint.
You are building a house (program). You need to drive nails. You create an instance of a hammer "object" following the blueprint described by the "class" definition. Now you can hammer nails.
A class generally has an interface and an implementation. This allows you to (and others) to call the code on your object having only to (generally) look at the interface.