Definition
Solo mining means your mining hardware works directly on constructing and hashing block candidates without pooling hashrate with other miners. If your miner finds a valid block hash, you receive the full block reward (currently 3.125 BTC plus transaction fees).
For most miners, especially those with consumer-grade hardware or open-source miners like the Bitaxe, solo mining is essentially a lottery. The expected time to find a block solo can be years or decades, but the appeal is the chance of winning the full reward. Many enthusiasts call this lottery mining.
In Simple Terms
Mining on your own without a pool. Low odds but you keep the full block reward if you win.
Mining Bitcoin independently without joining a pool. The miner receives the entire block reward if they find a block, but the probability of finding one is very low for small miners.