A fruit of the citrus family. Limes were probably brought from Indonesia/Malaysia area through Asia to Persia (around 1000-1200) and then began to be taken back to western Europe by returning crusaders, probably as early at the 13th century.
The most common variety of modern lime is a cross of lemons and limes, making them larger, juiceier, and slightly less sour than period equivalents. The bumps on the end of the lime (like on clasic pictures of lemons) distinguish this variety from older varieties. However only truly fussy authenticists are likely to even know this, let alone care about this difference, so keep using those limes in your feast for now.