My gums are able to come away from my teeth on the bottom. Is this normal? What should I do?

No. Healthy gums should be firm around your teeth and have a pink color. I would recommend seeing your dentist to determine the cues of your gums pulling away from your teeth.
Perio evaluation. If your gums are light pink, not red or inflamed, flat, stippled and do not bleed at all even with proper tooth brushing and flossing and there is only a 1 to 2 mm space at the margin where they pull back, you may be ok. However, regardless you should see a dentist for a complete and thorough periodontal examination to determine the health of your gums and supporting bone. Gum disease?
Not normal. Healthy gingival tissue is bound tightly to the teeth and bone. Gingival tissue that is pulling away from your teeth is indicative of periodontal disease. You should make an appointment and see your dentist or periodontist at once.