I do know the core wallet downloads and sync the blockchain to the computer and then easily shows amount of monero one holds in this core wallet. But how can we create a light wallet for mobile and still be able to show updated balance without downloading the blockchain ?
Same like mymonero: How does mymonero web wallet work?
Instead of your wallet getting blockchain data and scanning it yourself, you give the service your viewkey and address and it does the scanning for you.
It has privacy drawbacks. The service can see your incoming transfers and amounts. It can not see the destination. However, it could make good guesses when you send to someone else registered on the same service (because it could cross-reference his list of received with yours). That's why the objective is to have people run their own micro-service which they will be ale to do soon when work on open-source back-end will be finished.
However, I imagine mass surveillance of those services and data analysis would require massive amounts of computing power :)