Hi there - I'm Dr. Sara. I'm a licensed veterinarian who works exclusively with dogs and cats.
While lumps and bumps can be due to a wide variety of causes, when I see them in between toes the very first thing that I think of is what we call an interdigital cyst. An interdigital cyst is an area of ingrown follicles and wax/oil glands in between the toes that can cause very large swellings in between the toes. Initially the inciting factor is a combination of individual variation (ie: some pets are just more likely to get this problem than others) combined with mechanical irritation on the bottom of the foot that causes the sebaceous glands to become obstructed and release their wax and oil inward rather than externally. In that case, the wax and oil build up in the space between the toes, causing inflammation and discomfort. These cysts are also very prone to becoming infected, in which case they often get very large in between the toes on the top of the foot and even rupture out the top of the foot with bloody discharge. Dogs often lick at these like crazy.
In most cases an interdigital cyst can be managed medically with a combination of antibiotics, anti-inflammatories, and topical therapies like foot soaks. In severe cases, we sometimes have to surgically debride and remove the tissue from in between the affected toes to "clean out" the lesion and allow the foot to heal.
Other types of masses on the feet can range from benign "non-cancerous" masses all the way through to very malignant tumors. We vets often have a good idea of how malignant a mass is just by looking at it and touching it, so your vet probably already has an idea of what exactly this lesion is. Ultimately, to know for sure what a mass is, we have to take a tissue sample and send it off for biopsy at the lab. This is the only way to know for sure what a mass is, and most importantly, whether it is cancerous.
Please let me know what other questions I can answer for you :)