The answer to 'why is my drain constantly running' is that you likely have a faulty or stuck drain valve. This is a common plumbing issue that can be caused by a buildup of debris, a worn-out valve, or a problem with the valve's seal. The constant running water can be very wasteful and lead to higher utility bills.
To fix this, you'll first want to inspect the drain valve and clean out any debris that may be preventing it from closing properly. If the valve is damaged, you may need to replace it. This is a relatively simple DIY repair, but if you're not comfortable doing it yourself, it's best to call a professional plumber to take a look.