The ADX token is used for staking if you're running an AdEx validator. Staking your ADX will register your validator in a global registry where your visibility will be proportional to your staked amount.
The staked amount will be slashed if your validator misbehaves (i.e. an economic punishment will be applied to the misbehaving validator).
We are currently working on the specification of the AdEx Registry, however you can track the progress here.