A piece of rubber that's used to fill the bit of space between two parts of an engine is called a gasket. If your car has an oil leak, with any luck you'll just need to replace a gasket.
The job of a gasket is to prevent leaks and form a seal between two surfaces, usually the parts of a machine or system. Plumbing requires gaskets to prevent water seeping between pipes and fittings, and your car relies on its head gasket, which sits between the cylinder head and engine block, to keep it running. Colloquially, to "blow a gasket" means to get furious or extremely upset.