OMG Network first became public in 2017 under the name OmiseGo. It is one of the first working implementations of the Plasma scaling solution for Ethereum. The way Plasma works is that it processes transactions in batches on a sidechain and bundles them when they all need verification, in a process known as sharding. Implementing sharding on Ethereum natively is one of the long-term goals but its complexity makes it more feasible to implement it as a layer-two solution, which OMG Network set out to do.
For performing transactions and value transfers, as well as securing the side chain with staking, network participants use the OMG utility token. In other words, OMG is needed to use the network and participate in its maintenance for rewards.
The project has changed hands and management a few times already. Presently, the official resources maintain that the project has a new name, OMG Foundation, and is a fully-fledged layer-two ecosystem.