What causes swollen feet and ankles. They are so puffy I can indent them?

Lmultiple causes. Vein obstruction (gravid uterus e.g.), kidney disease and liver failure causing low Albumin leads to edema and heart failure with high venous pressure can all lead to edema. You should see your doctor for an evaluation and explanation.
Many causes. There are many causes for swollen feet and ankles, which is referred to as bilateral lower extremity edema (ble edema). Congestive heart disease, which is a condition of weakened heart muscle can be a cause. Venous incompetence, in which the veins of the legs become a little leaky is perhaps one of the more common causes. This is especially true if the edema is dependent or worse with standing.
Venous insufficiency. Meds as well as problems with the veins returning blood to the heart known as venous insufficiency.