A sponge absorbs input into a 1600-bit state through the Keccak-f permutation and squeezes output from it. The state splits into a rate (the part touched by input and output) and a capacity c that sets security; SHA3-256 uses a rate of 1088 bits and a capacity of 512. Because the capacity is never output, SHA-3 is immune to length extension, and SHA3-256(key ‖ message) is a sound MAC construction, though KMAC is the standardized one.
Test vector: SHA3-256 of the empty string is a7ffc6f8bf1ed76651c14756a061d662f580ff4de43b49fa82d80a4b80f8434a. Ethereum's "SHA3" is Keccak-256 with the original padding and gives a different digest; FIPS 202 added domain-separation bits.
SHA-3 is slower than SHA-256 in software on CPUs with SHA-2 instructions: about 1.01 GB/s for SHA3-256 against 2.85 GB/s for SHA-256 on one Apple M4 Max core with OpenSSL 3.6.5. It was standardized as a structurally different backup to SHA-2, not a replacement, and its SHAKE functions are the main hashing primitives inside ML-KEM, ML-DSA and SLH-DSA.