Objects are a bit more abstract than functions. A function is exactly what it means, even in mathematical terms: for a given set of inputs, a function will give a certain output.
i.e. f(x) = 10x is a function
Code
def foo(x):
return 10*x
As Pumbles said, in broader terms, functions are actions, much like verbs in a sentence.
Objects are a construct that we use to represent different *things* in a program, like we'd use nouns in a sentence. You may perform actions on them, and they may perform actions on themselves or on each other.
A class (of objects) is like a category of them. A class defines the shared traits of all the objects in this category. For example, an Integer might be considered a class, and you might have some Integer objects (aka "instances") such as 1, 2, 3, 4, 5, etc.
Typically, the most confusing thing about Objects and Classes is understanding the difference between them. The simplest analogy that you can understand them with is that a Class definition is sort of like a blueprint, while objects/instances are what get created from this blueprint. As in the example above, you can create as many different Integer objects as you like (1, 2, 3, 4, 1, 1, 1, 1), but the class of Integers itself is unique. There is exactly one kind (class) of animal called a giraffe, but there are many (instances of) giraffes in the world.