An internetworking layer (or internetwork layer, for short) is the key protocol used in the protocol suite used on an internetwork ('internet', for short - note the lack of the capital letter used for the Internet); it offers direct datagram carriage across the entire internet.
This layer/protocol usually provides an unreliable service, one which makes no guarantees that packets carried by it will not be delayed, damaged, duplicated, re-ordered, or lost completely.
This lack of any delivery guarantees makes the job, and implementation, of routers, the packet switches that form the lowest layer of the internet's infrastructure (along with the physical networks that connect them), much simpler.
It does mean that it is the job of the protocol(s) above the internetworking layer/protocol to ensure reliable data carriage on an end to end basis (if the application using that protocol needs such); they do so using checksums, sequence numbers, acknowledgements, timeouts, and re-transmission.
Each individual physical network has a protocol which specifies how packets are carried from one interface to that network to another; these protocols will vary from network type to network type. The internetworking layer serves to insulate everything connected to the internet from these variations; it is the same for all hosts and routers throughout the internet.
Since usually there are also a number of different protocols, providing different services, running on top of the internetwork layer, the internetwork layer is thus spoken of as being the 'waist' in the 'hour-glass' of that protocol suite. It is the one indispensable protocol that every node in the internet must understand and use.