Example 1:

I’ve been applying to several jobs in the last week. Many of
them require advanced degrees, which is something I don’t have. However, I do
have many years experience in the industry. I’ve been told not to bother
applying for those jobs because I’m not qualified, but I still think I should
try. I understand that and I know it’s a
long shot, but I’m hopeful.

Example 2:
Jack: The Powerball Jackpot reached 2 billion dollars! Are you going to buy a ticket?
Jill: No way. I never play the lottery. It’s a waste of money.
Jack: Of course it’s a long shot, but wouldn’t it be amazing to buy a 2-dollar ticket and win
2 billion?! I think it’s worth it for the excitement alone!

Explanation:
A long shot is something that probably won’t happen, but is worth trying for despite that. 

In example 1, the speaker is applying for jobs that have a specific education
requirement. Although he knows there’s a chance it won’t work, he will try
anyway. 

In example 2, Jack knows he probably won’t win the lottery, but he thinks it’s worth trying anyway.
This expression is often used with it is in the contracted form It’s
IT’S a long shot, but I’m going to apply for that job.
It is also used with be verb.
Winning the lottery IS a long shot, but I’m going to play.

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