A solo staker is someone who runs their own validator and locks up their own coins directly on a proof-of-stake network, without handing them to a pool, exchange or staking service. On Ethereum this requires 32 ETH and a computer that stays online. The practice is explained in full on the Solo Staking page.
Solo stakers keep all the rewards and full control of their keys, but carry the risk of penalties if their node goes offline or misbehaves. Alternatives include staking pools and liquid staking.