This is called the chronostratigraphic time scale -- that is, the division of time (the "chrono-" part) according to the relative position in the rock record (that's "stratigraphy").
The science of paleontology, and its use for relative age dating, was well-established before the science of isotopic age-dating was developed.
Unlike the continuous ticking clock of the "chronometric" scale (measured in years before the year AD 2000), the chronostratigraphic scale is based on relative time units in which global reference points at boundary stratotypes define the limits of the main formalized units, such as "Permian".
The chronostratigraphic scale is an agreed convention, whereas its calibration to linear time is a matter for discovery or estimation. We can all agree (to the extent that scientists agree on anything) to the fossil-derived scale, but its correspondence to numbers is a "calibration" process, and we must either make new discoveries to improve that calibration, or estimate as best we can based on the data we have already.
Relative-age time periods are what make up the Geologic Time Scale.
That last, pink Precambrian column, with its sparse list of epochal names, covers the first four billion years of Earth's history, more than three quarters of Earth's existence. Paleontologists have used major appearances and disappearances of different kinds of fossils on Earth to divide Earth's history -- at least the part of it for which there are lots of fossils -- into lots of eras and periods and epochs.
On Earth, we have a very powerful method of relative age dating: fossil assemblages.
Paleontologists have examined layered sequences of fossil-bearing rocks all over the world, and noted where in those sequences certain fossils appear and disappear.
Long before I understood what any of it meant, I'd daydream in science class, staring at this chart, sounding out the names, wondering what those black-and-white bars meant, wondering what the colors meant, wondering why the divisions were so uneven, knowing it represented some kind of deep, meaningful, systematic organization of scientific knowledge, and hoping I'd have it all figured out one day.
This all has to do with describing how long ago something happened. There are several ways we figure out relative ages.