From the Italian, literally translated as 'in the fresh'. In English, used to mean either 'in the open air' or, where specifically related to mural painting, 'on fresh plaster'.
The term is sometimes hyphenated; sometimes written as 'alfresco'.
I occasionally get irate correspondence along the lines of "You ignorant xxx, it means 'in jail'. Can't you speak Italian?". Well, no, I can't speak Italian - but I can speak English. Whatever the phrase means in Italian it has been adopted into English with the above meanings. Almost always, it is used in relation to dining alfresco, i.e. eating outdoors.
Both meanings have been in use in English since at least the late 18th century; for example, in Mrs. Eliza Haywood's History of Jemmy and Jenny Jessamy, 1753:
"It was good for her ladyship's health to be thus alfresco."
The earliest painting reference is in Thomas Harmer's Observations on divers passages of Scripture, 1764:
"It is superior to the al~fresco, and the Mosaic work."
Frescos are those paintings that are painted on walls and ceilings, in plaster that is not quite dry, so that the paint is absorbed into the surface layer. Probably the most celebrated example is Leonardo da Vinci's Last Supper.