Does "atmospheric forcing" have a stated definition?
The example that you've linked to (Larsen, 2003, "An investigation of the Faroe Shelf Front", Univ. of Bergen) is a description of various processes that contribute to the existence and variability of an ocean front around the Faroe Isles.  As an oceanography thesis, it's mainly concerned with the ocean state (e.g., temperature, salinity) and local, internal process that affect the front.  But the introduction also mentions external process that affect the local ocean state, such as the wider-scale ocean state/fluxes, topography and atmospheric forcing.

You could loosely think of these three respectively as the lateral, lower and upper boundary conditions for the local block of ocean of interest around the Faroes. In this context it could also be phrased as the forcing of the ocean by the atmosphere, so how the ocean is affected by the exchange with the atmosphere of quantities such as heat, water and momentum.  Larsen summarizes these through descriptions of air temperature and heat flux, precipitation, evaporation and runoff, and wind speed and direction.

Often when we're interested in a particular physical realm (e.g., atmosphere, ocean, land or ice-sheets) we prescribe (i.e., force) the interactions it has with the other realms to make it easier to investigate processes within the realm.