Yes, biology allows you to build farms on flat land squares that have no access to fresh water and aren't a bonus food square like wheat, rice or corn. These farms give 1 extra food on top of the normal output of the tile. If the farm is somehow connected to fresh water (lake or river), either directly or through a link of farms, then it gives 2 extra food on top of the normal output of the tile. Farmed rice, wheat and rice have a special output which is also increased by 1 for irrigation and 1 for the biology bonus.
Before biology but after civil service, you can only build farms next to a river or lake or adjacent to such a farm. These farms increase the food output of the tile by 1. Before civil service, you can only build farms next to a river or a lake and they increase the food output by 1.
Only tundra connected to a lake or river, plains, graslands and floodplains can ever be irrigated.