Serum (SRM) is a permissionless decentralized exchange (DEX) built on the Solana blockchain. Serum’s stated goal is to "bring the speed and convenience of centralized exchanges to DeFi while remaining fully trustless and transparent.” Part of the final vision for Serum is being fully interoperable with Ethereum, meaning users can interact with Ethereum’s blockchain using the speed and low cost of Solana. Serum is acting as the backend of DeFi for this ecosystem; they’re even reserving 20% of their fees to support projects that are hosting activity on the exchange and building interfaces for users.
Since it is built on a high speed chain like Solana, it can offer things most other DEXs cannot, including: sub-second trading and settlement, fully on-chain order books similar to traditional centralized exchanges, and fees at fractions of a penny. Serum has prominent names supporting it, as it’s backed by the people who made Alameda Research, FTX, Compound, etc., and it has enlisted large market maker Jump Trading to provide liquidity (a common problem for DEXs).
Serum is currently working on phase 3 of their roadmap, which involves building out many of the common DEX features, such as yield harvesting, borrowing and lending coins, margin trading, and building more cross-chain bridges. SRM is currently just under $1.2B market cap.
TL;DR: Serum is a permissionless DEX built on Solana offering some of the fastest DEX functions, completely decentralized derivatives exchanges, and trustless cross-chain trading.