It is described by Rex Owen, as its name suggests, as being "just like GPS, but for time". It can track the position in time and space of any pre-programmed object, and can also give the approximate current time and location of the user. In the case of Rex's TPS, the only thing it is set up to track the position of is his parents. At least Rex's handheld TPS has only a limited range of detection, as the signal of the tracked object gets fainter the farther away in time it is, and can disappear completely if it travels too far away.
As observed by Reese, it also contains the technology to see into other time periods.
It is first seen in Alien Parent Trap when Rex checks it after Max's house is stolen by Gavro. Dr. Ancient had given it to Rex in case they ever got separated, as seen in a flashback. It is used throughout Mesozoic Meltdown to track the D-Teams' parents, and ergo the Space Pirates, throughout time, and is the primary way the D-Team tracks down the locations of the Cosmos Stones, knowing that the Space Pirates will be in the times and places where the Stones can be found.
Reese also managed to use it to lock onto the Backlander's time and space coordinates from the D-Lab to communicate with the D-Team at various intervals throughout Series 2; however, the relative passages of time between conversations for the two groups were often very different.