In general, a gateway is a device on a network that acts as an entrance to another network. In more technical terms, a gateway is a routing device that knows how to pass traffic between different subnets and networks. A computer will know some routes (a route is the address of each node a packet must go through on the Internet to reach a specific destination), but not the routes to every address on the Internet. It won't even know all the routes on the nearest subnets. A gateway will not have this information either, but will at least know the addresses of other gateways it can hand the traffic off to. Your default gateway is on the same subnet as your computer, and is the gateway your computer relies on when it doesn't know how to route traffic.
If you don’t have a gateway your network communication have no problem. But you cannot communicate with other networks. That means your packet will not reach other networks.