The tokens issued by DAOs allow members of the organization to vote on certain decisions, projects or changes proposed to the organization. This system is also used to factor in the power of each voter. Typically, this means that the more tokens a member has, the more his vote will weight, although other aspects may also come into play.
This system acts as an anti-sybil measure, ensuring that one user can not vote multiple times without having to purchase more tokens from other members of the community (usually through an exchange). Since these tokens have a real-live value and can only be attain through an exchange or crowdfunding campaign, token holders who have a large stake in the organization have a direct benefit to behave in the DAO’s best interest.