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I was on a planet and I carefully observed the star of that solar system (its...

I was on a planet and I carefully observed the star of that solar system (its sun) and it had starspots that looked to travel from the bottom of the star to the top of the star. What does that tell me about the star and why?

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It tells you that the star is rotating itself about an axis parallel to your horizon of observation and from bottom to top(clockwise direction as you observe from right side of axis)

A schematic of rotation of star is as below,

Since sunspots appear for a period of time and they themselves do not move along the star surface any change in position of starspots can be attributed to the rotation of star about its axis. Thus here since the sunspots travel from bottom to top of star, it is rotating from bottom to top as shown in diagram.

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