The Ethereum Virtual Machine is the deterministic computer that executes smart-contract bytecode. It defines a stack-based instruction set, a 256-bit word size, persistent storage layout, and the gas costs of every operation.
The EVM is implemented identically on every Ethereum node, which is why state stays consistent across the network. It is also implemented (sometimes with subtle differences) by every "EVM-compatible" chain, BNB Chain, Polygon, Avalanche C-chain, Base, Arbitrum, Optimism, and dozens more.
For security, EVM compatibility is rarely exact. Differences in pre-compile addresses, opcode introduction timelines, gas pricing, and finality assumptions have all caused incidents in cross-chain deployments. Code that "should work on every EVM chain" should still be tested on every EVM chain.