Clicking will enable JACK transport. If disabled, Hydrogen will still use the JACK driver and registered audio ports. But it decouples its own transport state from the one of the JACK server and will not be in sync with other clients anymore.
Using Hydrogen can be registered as JACK Timebase Master and will send additional information, like the current speed, to other JACK clients. If it's registered as master, the button will appear checked (blue by default). If, however, another application, like Ardour, is registered as Timebase Master and Hydrogen acts as slave, the button appears checked too but is colored red. As soon as it gets unchecked (which can happen without explicit user interaction) Hydrogen works as a stand-alone JACK client.
The support of JACK Timebase can disabled in the Audio tab of the Preferences. This can be useful in the presence of a fault Master broadcasting nuisance information.