“I'd like to cancel my membership.”
You're a member of a gym. You don't use it very often, so you want to stop being a member. You go to the front desk and say this.
I'd like to cancel my membership.
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If you're a member of some service, like a gym, video rental service, etc. and you want to stop being a member, you have to "cancel your membership".
You can also use the phrase "cancel (one's subscription)" for subscription services like magazines or web applications, and "cancel (one's) account" for bank accounts, investment accounts, and so on.