How do I determine if a wall can be removed?
For the wall to be structurally important, it could 1) have a post located in it, 2) be a load bearing (vertical loads), or 3) a shear wall: 


Posts can support roof beams or second floor beams. You’ll need to look in the attic to see if a post extends up to a beam. You’ll also need to see if there is a footing in the crawl space directly under the post...however, the load from the post could be transferred to the floor without a footing. 
Likewise, roof joists or second floor joists could rest on this wall and you’ll need to look in the attic directly above the wall and in the crawl space directly under the wall. 
Shear walls are tougher to identify. However, because of the height and width, I can assure you it’s not a shear wall unless there is plywood on one side or both sides of the wall. 


Don’t forget to check for a plumbing pipes or electrical service lines in the wall that will need to be relocated. 

I’d check to see if there is a duct in the wall that connects to the floor register shown in the pic too...but it could be re-routed. 

You’ll also need to fill-in the floor material when the wall is removed. 

BTW, if the wall needs to stay (for an electrical line, plumbing pipe, etc.) you could keep the wall by turning the studs 90 degrees and reinstalling the gypsum board. (It could make a nice visual barrier too so you don’t need to look at the side of the fridge.)