Shares represent each staker's voting power. They are issued by the staking smart contract for its own accounting.
Shares are calculated based on the ADX that you’re depositing and the ADX already in the contract at time of depositing, therefore the number of shares a staker has is likely to be different from the number of ADX in their staking bond.
The reason for this is that the share to ADX value only goes up over time: e.g. on first stake ever it’s 1 ADX for 1 share. But then the contract incurs reward, so 1 share = 1.0002 ADX.
In the Ambire AdEx Staking portal, shares are represented as a percentage: