In what ways is a Kalman-filter a filter?

A Kalman Filter is a filter in the same sense as that used by the air defence system for the UK in the WW2 "filter room" where radar data from multiple sources was combined to form a tactical picture.

From the relevant Wikipedia page:

Radar detection of objects at that time was at its early stages of development and there was a need for a method to combine the different radar information gathered from different stations.

Accurate details of incoming or outgoing aircraft were obtained by combining overlapping reports from adjacent radar stations and then collating and correcting them. This process of combining information was called "filtering" and took place in seven Filter Rooms.

An elementary way of seeing it is that the Kalman Filter smoothes the trajectory of the variable given by the noisy measurements to make it approximate the real (non-zigzagging) trajectory. The spectrum of the Kalman-Filtered variable will be attenuated for higher frequencies, just as it will be after using a low-pass filter.