In a few words, Plasma is designed as a scaling solution technique for the Ethereum network. The main proposal of Plasma is to work as a framework of side chains that will interact as sparingly as possible with the Ethereum blockchain (the main chain). The Plasma structure is being designed to function as a blockchain tree, hierarchically arranged in such a way that many “child chains” are created on top of the main chain.
The Plasma framework is built through the use of smart contracts and Merkle Trees and enables the creation of an unlimited number of side chains - which are, essentially, smaller copies of the Ethereum blockchain.
In effect, the child chains are designed to run a customized smart contract, which makes it possible for companies to employ the Plasma structure according to their individual needs. Therefore, different Plasma smart contracts can be created for different use cases. By leveraging the security provided by the main chain, Plasma is able to deploy a multitude of different child chains that would be working in a predetermined way, towards specific goals (not necessarily related to those of the main chain). Therefore, the main Ethereum blockchain would be less likely to get congested.
In short, Plasma is an off-the-main-chain solution that seeks to drastically increase the efficiency of the Ethereum network (or any other blockchain) by taking the bulk of the processing duties off of the main chain and redistributing it onto a series of smaller, functional chains. 
Plasma was proposed by Vitalik Buterin and Joseph Poon, in August 2017 as a scaling solution for Ethereum, but the concept may be adapted and implemented into other blockchains as well. Poon was also one of the idealizers of the Lightning Network proposal, which explains the similarities Plasma and LN have as scaling solutions (Plasma for Ethereum and Lightning Network for Bitcoin). But keep in mind that they have different approaches and mechanisms.
The Ethereum Plasma is an open-source project and the public repository can be found on their GitHub. For more detailed and technical information, you may also refer to the official Plasma whitepaper. Although the project is still in the early stages of development, the idea is indeed very interesting. If successfully implemented, Plasma can drastically improve the efficiency of the Ethereum network. In addition, it may also be a useful starting point for other blockchain networks that may need a scaling solution going forward.

Note, however, that Plasma alone is not a project, it is a framework for building scalable applications that can be implemented in different ways by different research groups or companies.