If something's airtight, it is completely sealed so that no air can get in or out of it. When you make homemade jam with the raspberries you picked, it's important to make sure the lids are airtight so the jam won't spoil.
Many kinds of food and medicine you buy in a store are airtight. The airtight seal on a package, bag, or can assures you that the contents are safe from any germs that might get in and contaminate them. You can also use this adjective to mean "certain" or "indisputable," like an airtight alibi that can't be argued with, or an airtight plan that's guaranteed to work.