A member cannot attend an association's annual meeting but does not want their vote to disappear. Proxy voting lets them formally authorize another person to vote for them. The proxy may receive a precise instruction or some discretion, depending on the authorization and applicable bylaws.
The important distinction is permission. A recognized proxy is acting under an accepted process, rather than impersonating an absent voter. In UK elections, appointing a proxy involves formal authorization and eligibility requirements. An association likewise needs a recognized way to establish that an absent member authorized this person to cast this vote.
Someone present carries someone absent
A small association might require a signed form naming the meeting, the proxy holder, and any limits on their vote. Checking that record before voting helps prevent duplicate or disputed representation. Members also need to know whether the authorization can be withdrawn and whether one person may carry many proxies.
The last question matters politically. A well-connected member who gathers authorizations from many absent people can dominate a meeting despite few people being physically present. That may faithfully represent their wishes, or it may reflect how little they knew about the coming discussion. Unlike a full system of liquid democracy, a proxy arrangement can be limited to a single occasion without allowing ongoing, topic-specific chains of delegation.