The word airtight means impermeable to air. If a container is airtight, air can’t get in and air can’t get out.
If you ever find yourself in an airtight room and you can’t get out, how long you will survive depends on how big the room is and, therefore, how much air there is in it. Your respiration exchanges carbon dioxide for oxygen.
Because the room is airtight, the carbon dioxide can’t escape the room and new oxygen can’t get in. This is a situation that one would generally like to avoid if at all possible.
Airtight can also mean unassailable. If you have been accused of a crime, but you have an airtight alibi then you will be acquitted if you are being tried in a country that is governed by the rule of law.
If you are in a country not governed by the rule of law, being a friend of some of the people in power, or paying a sizable bribe, is often a better defense than an airtight alibi.