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A Community is an organization that seeks to facilitate the cooperation between at least two parties (referred to as its 'members') based on interests that these parties share as each of them seeks to realize its own, individual objectives. Facilitating such a cooperation can be expressed in terms of objectives that each of its members contributes to realizing.
Note that a single set of parties can seek different cooperations with one another, with different associated sets of objectives. They are then different communities (even though they have the same members), because it is conceivable that another party will join one, but not both of them, or one member will leave one, but not both communities.
A community is a specialization of the more generic ecosystem in the sense that it is an organization (which an ecosystem need not be) that (actively) facilitates the cooperation between its members, whereas in non-community ecosystems, this cooperation is not actively organized.
The ability to distinguish between communities and other organizations, which simply seek to realize their own objectives without any (explicit) regard to the objectives of other parties is particularly relevant in decentralized contexts. The characteristic of centralized contexts seems to be that an organization that seeks to facilitate cooperation between other parties has (and uses) an ability to force these parties into complying with rules, working-instructions, etc., which may or may not be aligned with the interests of each of these parties. Such organizations are usually referred to as 'authorities'.
In decentralized contexts, the assumption is that all parties are autonomous (self-sovereign), which means that whatever such parties do (not) do is outside the scope of control of an organization that seeks to facilitate cooperation between such parties. Such organizations will have objectives the realization of which do take the objectives and interests of other parties into regard.
A Community is an organization that has one or more objectives that seeks to facilitate the cooperation between at least two parties based on interests that these parties share as each of them seeks to realize its own, individual objectives.