Have you ever worked in finance before?
I have not but the exact definition is the field that deals with the study of investments, I find a lot of it to be so confusing but some people eat it up like peanutbutter!
I know, some many different terms, that I do not understand, do they have a name for people that study this or work in the field of fiances?
It really depends on the field, there are three sub categories that finance can be broken into, public finance, corporate finance, and personal finance. I imagine each subcategory has a different name and companies may have different financial needs and some special titles. 
I see, it really does have a lot to it. What exactly is public finance?
Good question, public finance is the study of the role of the government in the economy. So think allocation of money and resources and government basically.
I see, I feel like our government may not be doing the best job there! So is corporate finance more about big businesses? 
Correct. It is the area of finance dealing with the source of money and capital of corporations. It also includes the actions anagers take to increase the value of the firm to shareholders of that firm and the tools and analysis used to allocate financial resources. There's so much to it it has its own subcategory!
My goodness, I never realized it went so deep. Is there a name for the study of finance or colleges dedicated to studying finances?
Finance aka the science of money management would be the main one, also business would also be one. I could also see accountant work being involved but i would say its just finance and/or business management!