"Security" means guarding or protecting things. For example:

• "Airport security" is guarding an airport.
• "The Department of Homeland Security" is a government department in the U.S. which is in charge of protecting the country from terrorism.

When you describe security as "tight", it means that officers or security guards are watching something really carefully. When security is tight at an airport, it means that the security guards do extra checks like searching through people's bags and making them take their shoes off.