Injection/infusion play involves insertion of a standard hypodermic needle under the skin followed by injection (small volume) or infusion (larger volume) of sterile saline. The sterile saline used is specifically meant for injection and should not be confused with sterile saline for irrigation or sterile contact lens solution.
In ponyplay (and petplay), a pony's vet (or trainer/owner) may inject a small volume (~ 1-5 mL) of sterile saline as a "vaccine" or, less commonly, as "sedation" for further veterinary procedures. This type of injection play, when done properly, is relatively safe and fairly painless (depending on the injection site).
For these reasons, injection play is often done for show and to add to the realism of a scene. However, it is still a powerful psychological tool that can reinforce the bottom's status as an animal, especially when combined with physical restraint or other scene elements. For example, as a prelude to castration play (e.g. an injection of sterile saline administered to the scrotum or surrounding area as an "anesthetic" prior to castration), injections can add to the intensity of a scene.
Infusion play is essentially the same as injection play except that a larger volume of fluid is administered. The administration of a larger amount of fluid results in swelling and heightened sensation in the area. Also, in infusion play the fluid is most often infused into the scrotum, labia, or breasts.
Infusion of saline in ponyplay or petplay can be done as part of a veterinary procedure (it's actually relatively common for biological animals to have subcutaneous infusions of saline or LRS to combat dehydration due to illness. Indeed, it's much more common in outpatient veterinary medicine to administer fluids subcutaneously than it is in human medicine), a cosmetic veterinary procedure (e.g. to increase the size of a pony's balls to more closely mirror those of a bio-horse), or as a part of sensation play.
A couple important points about injection and infusion play:
If you want more information on infusion and inflation play, Mistress160 has a good article on saline infusion play in BDSM that is definitely worth a read. Scrotal inflation play using argon (inert gas) is also briefly discussed in that article.
Places to buy infusion play supplies: