A lamport is the smallest unit of SOL, Solana's native token: one billionth of a SOL, or 0.000000001. Everything Solana meters (transaction fees, rent deposits, account balances) is stored as a whole number of lamports.
The short answer
One SOL equals exactly 1,000,000,000 lamports (10⁹). Like Bitcoin's satoshi and Ethereum's wei, the lamport exists because blockchains do arithmetic in integers: balances live in u64 fields counting lamports, and the nine-decimal SOL format is a display convention layered on top.
Nine decimals (rather than Ethereum's eighteen) keeps the numbers compact while still being fine-grained enough to price fees that cost fractions of a cent.
Named after Leslie Lamport
The unit honors Leslie Lamport, the computer scientist whose work underpins essentially all of distributed computing: logical clocks and the ordering of events, the Paxos consensus algorithm, Byzantine fault tolerance, and, on the side, LaTeX. He received the Turing Award in 2013.
The homage is pointed. Solana's signature idea, proof of history, is a mechanism for ordering events in a distributed system, the exact problem Lamport's 1978 paper "Time, Clocks, and the Ordering of Events in a Distributed System" made tractable. Naming the atomic unit after him is the network citing its sources.
Where lamports show up
Fees. The base fee is 5,000 lamports per signature: 0.000005 SOL, a fraction of a cent at any plausible price. During congestion, transactions add a priority fee priced in micro-lamports per compute unit, a millionth of a lamport, which tells you how small Solana's fee granularity gets.
Rent. Every Solana account must hold a minimum balance proportional to the data it stores to be "rent-exempt". The deposit is quoted in lamports: roughly 890,880 lamports (~0.0009 SOL) for a zero-data account, about 2 million lamports (~0.002 SOL) for a standard token account. The rent calculator computes it for any size.
Balances. RPC responses return lamports everywhere. If you query an account and see 1500000000, that is 1.5 SOL; the decimal is yours to place.
One naming collision to watch
The abbreviation mSOL is overloaded: as a unit it means a thousandth of a SOL, but in DeFi it is also the ticker of Marinade's liquid-staking token. Context usually disambiguates (unit tables mean the former, token lists mean the latter), but when in doubt, count the decimals. This is one reason lamports, which are unambiguous, remain the professional unit of record.