To be able to do anything with/on Adopt a Backpacker, you must first have an account. If you can successfully login to Adopt a Backpacker, using an username/email plus a password, then you have an account. Congratulations!
A profile is all the extra information you add about yourself, i.e. to your account.
Some of this profile information is required, e.g. date of birth, nationality, language(s) you speak, etc. Other information is optional, e.g. photos, interests, etc.
There are different profile types: backpacker, au pair, local friend, employer, etc. Depending on which profile type you choose, there may be the opportunity to add more or less information, required or optional, to be more relevant and helpful for that profile type.
Hint: profiles that are fully complete and up-to-date will have more success on Adopt a Backpacker than those that are less complete.
Your membership plan is sometimes referred to as just "your membership" or "your plan", but it all means the same thing. It defines what benefits you get with Adopt a Backpacker. It could be free or paid, basic or premium. Every account must have a plan.