A "membership" represents you as an individual person (not a company, group, club, or organization). It's how you identify yourself to us, and how you access our services. If you're a US worker, it's like your social security number except, you know, less social and more secure. And, in most cases, less number-y.
An "account" is how you pay for our services. It contains the funds that you use to purchase hosting. You'll need at least one. You may create more, if you want, but you don't have to. Accounts also hold hosting-related assets, like web sites, domains, and database processes. Just as one membership can have several accounts, one account can fund several different assets.
Accounts also contain contact information about their owners, which may or may not be the member who manages the account. A web designer managing an account for a client would be a good example of a case where the member who manages the account is not the owner. Similarly, a company might own an account, even though it's managed from the company's webmaster's membership. Keep in mind that from our perspective, regardless of account ownership, the member is the only representative of the owner authorized to access the account. (There's no point in having any other policy, since the member can change the account's contact information at any time.)
People use accounts to group related stuff together, to separate business and personal expenses, or to keep track of multiple clients. All sorts of reasons. Other people are perfectly happy to jam everything into one account and have only one balance to keep track of.
It's a little like a bank. You are one person, but you might have two savings accounts: one for college, and one for "rainy days." The bank (if they know you at all these days) knows that you are just one person, and you have your social security number (membership) to prove it.
Unlike accounts, you may not have more than one membership. That would be like opening an account at your bank, then going out to your car, putting on a fake moustache, and going back in to open a second account.* Even if you could, why? Likewise, you cannot go into the bank, give them someone else's social security number, and open an account in their name.** So please don't open memberships for other people here.
*At least, we assume it's like that, but we've never actually tried it. Our bank has a pretty good sense of humor, but why push our luck?
**Sense of humor or not, we're pretty sure that's a felony.