Simple Explanation of orbitals
Well, the first step is to stop thinking electrons as being very small balls that orbit around the nucleus in a circular path. This is known as the Bohr model. Despite this model being an excellent model at an introductory level, it doesn't tell the entire story.



There are several issues with the notion that electrons travel in a circular orbit around the nucleus, the main one being that they should eventually undergo orbital decay and hence eventually slow down and crash into the nucleus. Of course, this doesn't happen. So how do electrons move around the nucleus?

This is where quantum theory came to the rescue in the early 20th century. It stated that electrons could not be treated as a classical particle and didn't not have a definite position and momentum. So this basically means that we can't exactly know an electron's position and its momentum at the same time. This relationship is given by the Heisenberg Uncertainty Principle. 

I won't go into detail about it since to keep this explanation basic, but if you are interested check out this video which provides a really good explanation.  

So basically what quantum theory tells us that we actually can't specify where and what a path an electron is going to take. However the Bohr model assumes that you can precisely plot out where an electron is going to be, but we now know that due to the Heisenberg Uncertainty Principle you can’t precisely know the exact position and momentum of an electron. So we actually can't construct an orbit and say that the electron is always going to follow that path.

Therefore, it makes it impossible to plot an orbit for an electron as how can you? If you don’t know where the electron is going to be next, there is no way you can predict its path. 

So how can we get around this problem? Well, if we can’t draw the orbit for an electron the next best thing we can do is to plot an electron density probability orbital for it. Also known as atomic orbitals. 

An orbital is a well defined region of space. Therefore an atomic orbital is a region of space that shows where the electron will be 95% of the time (usually we take 95% but it could be any number really such as 90% or 75%). 

A simple way of thinking of orbitals is that imagine that you have a magic camera that can take a sequence of photos of an electron in a hydrogen atom. The electron appears as a dot. Now if we superimpose all of these images, you will see something like this:

 

Since we generally take atomic orbitals to be the region of space that shows where the electron will be 95% of the time, the very outer sphere of the above image is said to be the orbital of the electron.

Hopes this helps you understand orbitals. If you have any question, feel free to ask.