The Geologic Time Scale is up there with the Periodic Table of Elements as one of those iconic, almost talismanic scientific charts.
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.
Just like a stack of sedimentary rocks, time is recorded in horizontal layers, with the oldest layer on the bottom, superposed by ever-younger layers, until you get to the most recent stuff on the tippy top.
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.
When you find the same fossils in rocks far away, you know that the sediments those rocks must have been laid down at the same time.
When you talk about the Precambrian, Paleozoic, Mesozoic, and Cenozoic on Earth, or the Noachian, Hesperian, and Amazonian for Mars, these are all relative ages.
Relative-age time periods are what make up the Geologic Time Scale.
There are absolute ages and there are relative ages. We use a variety of laboratory techniques to figure out absolute ages of rocks, often having to do with the known rates of decay of radioactive elements into detectable daughter products.
Unfortunately, those methods don't work on all rocks, and they don't work at all if you don't have rocks in the laboratory to age-date. They are descriptions of how one rock or event is older or younger than another.
There's no absolute age-dating method that works from orbit, and although scientists are working on age-dating instruments small enough to fly on a lander (I'm looking at you, Barbara Cohen), nothing has launched yet. Relative age dating has given us the names we use for the major and minor geologic time periods we use to split up the history of Earth and all the other planets.
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.
When you talk about something happening in the Precambrian or the Cenozoic or the Silurian or Eocene, you are talking about something that happened when a certain kind of fossil life was present.