Once we got info on our star about its behavior and how it changed, we can deduce a few things
If it was just eclipsed by something which is common to identify exoplanets with it: it's a blockage of the light we received
Measure distance: depends on how a star pulses. Longer pulse, larger star
Define what change is happening on the star (intrinsic or extrinsic): we can know if a star is dying, identify any kind of "Novae", suffering an eclipse
Define if a star has a regular or irregular pulse (how much light do we receive in a period of light): Regular means it has a cycle. Irregular: It can have sudden drops or high light emissions
If it's getting closer or further: depends on the light color, red is going further, blue is closer and closer