Probably the best definition of invention is a device, contraption, or machine that changes our way of doing things, that no one else has thought of, and that generally has a patent taken out on it so no one else can copy it or get royalties from it.  Inventions usually come about because someone gets tired of doing something a certain way and wants to do it faster, more efficiently, or better.  It can be a long process, however, and is usually fraught with much trial and error, so inventors have to have stamina, drive, determination, and resolve to keep on trying until they achieve the results they're looking for.

But, sometimes inventions come about entirely by mistake!  Perhaps too much or not enough of a particular ingredient is added to something, making an entirely new product that proves to be unique and useful.  Sometimes inventions come about by inspiration, such as in a dream, an epiphany, or a vision.  At any rate, inventions are the "brain child" of inspired people and we're glad for them!

Innovationsare entirely different than inventions, in that someone takes something already being done and finds ways to make or do it better.  BusinessDictionary.com defines innovation as

the process by which an idea or invention is translated into a good or service for which people will pay, or something that results from this process.

For example, Thomas Edison invented the incandescent light bulb.  It's said that he tried over 2,000 times before he obtained a workable model and that it took years to achieve.  That was his invention, and it came about in increments.  Then, years later, someone found out how to switch the light bulb from incandescent to fluorescent, and then to halogen and LED.  This process was quite a substantial change and literally happened overnight!  The basic principle of the light bulb is still the same and the original patent belongs to Edison.  But, others took that principle a little further and expanded it into other lighting forms.  This is innovation.

You can't have invention without innovation, and visa versa. 

An invention is something that has been created for the first time.  An innovation is the first time that a given thing has been used in a particular way.  An invention is in some ways theoretical whereas an innovation is practical.

An inventor comes up with an idea first.  But that inventor may not have any practical use for his or her invention.  It is simply a piece of technology that has never been created before.  An innovator takes something that has already been invented and figures out a way to use it that is really practical.

Because of this, innovations have more of an impact on society.  An invention has no real use until some innovator (who could be the same person as the inventor) figures out a way to make it useful and to make it available to a broad market of consumers.