An account is tied to a pricing tier, whether that's the free tier or a paid one. Check the pricing page for details of the different pricing plan.
There can be multiple users within an account, and API requests are saved against an account. This allows API requests to be shared between team members.
When you sign up in the Data Fetcher app a default account will be created for you, called 'YOUR_NAME's account'. You may also have been invited to other accounts, e.g. by a team member.
A user is simply a name, email and password. A user can be in multiple accounts and an account can have multiple users.