What is a test case? how we use it to check the software?

What is  a test case? how we use it to check the software? Kindly give any example of test case?

A test case in software engineering is a set of conditions or variables under which a tester will determine whether a software system is working correctly or not.

Below are different test case for your VU Mail login page, for example:

1. Try to login without entering any username and password 
2. Try to login only with Username 
3. Try to login only with password. 
4. Try to login with correct user name but wrong password
5. Try to login with correct password but wrong user name 
6. Try to login with right username and right password and see if you are logged into the system or not
7. Try to login by enter long username and password that exceeds the set limit of characters. 
8. After successfull sign-out, try “Back” option from your browser. Check whether it gets you to the “signed-in” page.