So what is the purpose of this piece of tack? It protects the horse's belly from getting hit by the front hooves while jumping. Some horses fold their front legs up so much that the hooves contact the belly and this can cause the horse pain or injury, especially if the horse is wearing studs. Most belly pads have a snap, ring or narrow piece of leather for the attachment of a breast plate or martingale.
How do you know if your horse needs one? You will need someone to watch your horse jump over a period of time to see what sort of front leg technique he has. Some horses hit themselves so hard that you will actually notice them hanging their front legs over the next jump after hitting themselves in order not to do it again. If you notice that your horse is doing this, he would probably appreciate a belly pad. If you notice marks in the middle of your girth after jumping, your horse is probably hitting himself.
A horse with front end technique like this one would most likely benefit from using a belly pad, especially since he is wearing large studs in his front shoes. The belly pad would extend further forward than the current girth to protect the area that you can see is about to be hit. The hooves will, in addition, hit different areas at different points of the jump so a single photo like this one will not tell you exactly where the horse needs extra protection.
If you aren't sure whether or not your horse needs a belly pad, there's no real harm in using one anyway apart from the higher price and the increased tack cleaning time (the larger surface area attracts a lot of mud!).