Thank you for your question.
The simplest definition I uncovered by far is as follows on this page
viewed as html (the pdf is not working at the moment so I relied on
the html version):
A finite automata is a collection of three things:
1. A finite set of states, one of which is designated as the initial
state,called start state, and some (maybe none) of which are
designated as final states.
2. An alphabet S** of possible input letters, from which are formed
strings, that are to be read one letter at a time.
3. A finite set of transitions that tell for each state and for each
letter of the input alphabet which state to go to next..."
**NOTE: This is actually the Greek letter Sigma which does not reproduce here.
As I am sure you have found, there are numerous more complex
defintions to be found, such as:
Thsi page on robotics at Berkeley University
But you might wish to see this definiton at a GSU page:
and this one in pdf format - go to page 6:
And this excellent page at Wikipedia:
"finite automata" +define OR definition
I trust my research has provided you with a simplified answer and
additional defintions to provide greater detail. If a link above
should fail to work or anything require further explanation or
research, please do post a Request for Clarification prior to rating
the answer and closing the question and I will be pleased to assist