Account/accounts is something a person has with a company - like a bank account or even facebook account.
Accounting is a profession or the area of a building that deals with the finance of a company - The accounting is responsible for taking care of the money of a company, for example.
Accountancy is the practice of keeping record of something (whether you do for your household or in a job) classyfying the papers and separating them accordingly.
There are many other professions in this world that do basically the same such as treasury, bookkeeping etc.
Hope it helps