So lets break this down. Footballfish (and many other Anglerfish) live in the deep sea. In this case, in tropical and subtropical waters around 3,300 ft. Footballfish display extreme sexual dimorphism, with the females being much, much larger than the males. This will come into play later. The females, with their large, round forms, are slow swimmers, and actually hunt by doing well, not much of anything at all. They have a rod known as an ilicium that has a biioluminescent bulb attached to the end. Due to the depth of water that they live in, the water is especially dark and this bulb attracts prey. Females are then able to snatch their meals right in front of them. They feed mostly off of small fish and cephalopods.
Females are also quite good at attracting potential mates. Remember those tiny male Footballfishes? Well, they never get very big, since they don't typically have the ability to feed, but they are able to track down females due to their great sense of smell and pheromones that the females emit. Once a male finds a much larger lady, he latches on to her with his mouth, and eventually his entire body dissolves into her, leaving behind only gonads which the female is then able to use to impregnate herself with. This comic sums it all up quite nicely (potentially NSW).
It should be noted that not all Footballfish species reproduce this way. Some species have males that are free-living. The whole "attach and dissolve" thing is also common in many other Anglerfish families.
Thanks to Eric for the suggestion!