die Mitgliedschaft
membership
The state of being a member of an association, a party, an organization, or a club.
Er hat seine Mitgliedschaft im Fitnessstudio gekündigt.
He canceled his gym membership.

membership
Loading your saved state.
membership
The state of being a member of an association, a party, an organization, or a club.
Er hat seine Mitgliedschaft im Fitnessstudio gekündigt.
He canceled his gym membership.

The word is made up of 'das Mitglied' (member) and the suffix '-schaft'. The suffix '-schaft' forms feminine nouns that describe a state or a community, as in 'Freundschaft' (friendship) or 'Mannschaft' (team).
Durch seine Mitgliedschaft wurde er Teil der Gemeinschaft.
Through his membership, he became part of the community.
To express where someone is a member, the preposition 'in' with the dative is almost always used. You have a 'Mitgliedschaft in einem Verein' (membership in an association), 'in einer Partei' (in a party), or 'im Fitnessstudio' (at the gym).
Die Mitgliedschaft in diesem exklusiven Club ist sehr teuer.
Membership in this exclusive club is very expensive.
Common verbs connected with 'Mitgliedschaft' (membership) describe its beginning, management, or end. Typical ones are: 'eine Mitgliedschaft beantragen' (to apply for a membership), 'kündigen' (to cancel), 'verlängern' (to renew/extend), or 'beenden' (to end).
Ich möchte meine Mitgliedschaft zum nächstmöglichen Zeitpunkt kündigen.
I would like to cancel my membership at the earliest possible date.
basis / base
'die Basis' and 'die Mitgliedschaft' can both have to do with the members of an organization. 'die Basis' means the ordinary members, as opposed to the leadership. 'die Mitgliedschaft' can mean either that someone is a member, or all members as a whole. It is more neutral and does not automatically mean there is a contrast with the leadership. Learners may confuse the words when talking about parties, associations, or clubs. For the ordinary members as a group, you are more likely to say 'Basis'; for the status of being a member, you say 'Mitgliedschaft'.

Für das Fitnessstudio habe ich eine Mitgliedschaft für ein Jahr abgeschlossen.
I took out a one-year membership for the gym.
Die Basis des Vereins unterstützt den Vorschlag des Vorstands nicht.
The grassroots of the association do not support the board's proposal.