Your engine creates a vacuum when the intake valve is partially closed in the intake manifold. The vacuum is then used to help power other components on the car. It may help reduce your effort in pressing down the brake pedal or, in older cars, it may even power the windshield wipers. If enough vacuum hoses have leaks, or you have one big leak, it may keep your old engine from starting.
In newer cars, some vacuum leaks can cause engine sensors to report incorrect readings to the engine's computer system. When this happens, even minor leaks could keep your engine from starting. A few trouble spots for vacuum leaks may be the throttle body, the manifold seals, the positive crankcase ventilation (PCV) valve or the PCV hose. Although those may be some trouble spots, there are numerous vacuum hoses in each car.
When the engine sits for a long time the hoses can deteriorate and develop cracks. A few small leaks won't keep your car from starting but large leaks, or too many small ones, may be too much. There are several ways to determine if you have a vacuum leak, but the most effective is using a smoke generator. This smoke-out tool generates smoke in the engine so you can see where the vacuum leaks are coming from in each hose.
This tool is somewhat expensive and usually used by professionals, so it may be a better idea to locate a diagram of your engine's vacuum hoses and replace them all instead. Replacing all of the hoses in an old engine isn't a bad idea, considering you could spend a lot of time trying to track down a leak and you'll be replacing several hoses either way.