'Period' is the American term used for the punctuation 'dot', otherwise called a full stop, at the end of a sentence. Here is one ----> .
If someone says 'Period' after making a statement, it means 'And that's the end of it' - No questions, no excuses.
For example. 'He's not good enough to get the job. Period.'
You'd say this to tell the people listening that you are not prepared to discuss this any more.