First thing you should do is get down on your knees and see if the latch lines up with the hole in the strike plate. If the latch doesn't seem too high or low, then it's likely that the latch isn't going into the strike plate hole completely. Adjusting the door stop might be one solution, so go to the opposite side of the door where you can see the door stop (the piece of trim that the door closes against) and close the door. Notice if the door hits the door stop evenly... or if maybe the door has warped and it is hitting in one spot (bottom or top?) first, which would prevent the door from latching. You can simply pry the door stop loose, move it a little, and that will let the door close a little farther and maybe it will latch. Just guessing here, but that might be a start. Instead of trying to move the strike plate a fraction of an inch, I've had good success using a rotary file on a drill, and grind a little out of the strike plate, enlarging the hole in the direction that would benefit the latch. Not sure if it's my imagination... but it almost looks like the latch might be low, judging from the wear marks on the strike plate.

What he said. Many older homes had 2x3 walls on some rooms, so a standard door jamb won't fit. Trim it down as suggested.

Thanks for the advice I will give it a try and let you know how I make out.