I know some of the MikroTik routers have GPS functionality built it. How is that typically used?

I know police/firefighters have software that will plot their position through some type of software that they use. Is that the general purpose?

If so, how/where does the MikroTik device send the GPS data? Is there some GPS API that MikroTik has? Or does it rely on scripting?

Not only emergency services have such software, commercial companies use fleet management systems with geolocation support too. There is no standard API, you indeed have to use scripting to deliver the geolocation information from the rolling stock to the fleet management system. There is an example on the manual pages.

Yet another possible use is to provide real time information to networks not connected to internet, but don't expect stratum 1 quality.

In case of LtAP mini, don't forget that an external GPS antenna is a must, not an option. The "big" LtAP looks happy with the internal one in my attic under roof tiles made of concrete.

It determines a position
Gives Navigates
Monitoring object or personal movement.

Accurate time source often required for a variety of systems. GPS provides this.

Accurate time source often required for a variety of systems. GPS provides this.

Not Mikrotik devices as they lack 1PPS support which is necessary for accuracy better than one tenth of a second.