Satoshis are the name for the smallest unit of Bitcoin.
For example, for USD we have Dollar = $1.00, Cent = 1/100 of a dollar ($0.01).
For Bitcoin, there's "bitcoin" which means 1.00000000 bitcoin, a couple more denominations (such as "mBTC" which is 0.001 BTC), and "satoshi" which represents 0.00000001 BTC. Satoshi is the smallest denomination and obviously was named after Satoshi Nakamoto, the creator of Bitcoin.