To understand sedimentary rock layers, it is important to understand that the earth's surface is always slowly - but constantly - changing. Mountains and other areas that are raised above the surrounding land are subject to wind, rain, and water which constantly wear them down. The bits of sand, pebbles, and rubble that get worn down from mountains, mesas, and cliffs are pulled by gravity to the low-lying areas (valleys, lake beds, sea-shores) where they collect over time. Over millions of years, these deposits can harden and petrify into sedimentary rock layers. Other sedimentary rock layers (like limestone) form on ancient sea or lake beds and are the remains of the various animals and plants that lived in the water.
Thus when you look at the different layers of the Grand Canyon, you are looking at the petrified remains of what was once the surface of the earth (or the bottom of a sea bed) at a time the region was being covered with sedimentary material. Different rock layers occur when changes to the environment cause one type of material to stop being deposited and new materials get deposited instead. For example, a shallow sea may create layers of limestone. If the sea later dries up and the now exposed sea bed gets covered over with blowing dry sand, then a layer of sandstone will be deposited on top of the limestone. In this way, geologists can see how the surface of the earth changes at a given spot over time.
As for the specific rock layers in the Grand Canyon, here is a VERY SIMPLISTIC description of the situation and processes that produced the major rock layers (from the oldest layer at the bottom to newest at the top):
Vishnu Schist (bottom) - 1.7+ billion years ago the area around Grand Canyon was a series of volcanic islands surrounded by a shallow sea. The resulting deposits of ash, sand, and mud created shales, sandstones and mudestones that were eventually compressed and distorted with time and pressure into gneiss and schist.
Tapeats Sandstone - There is a long period where the rocks from this area did not survive and so no record is left (the Great Unconformity). Eventually this area became part of the edge of the still forming North American continent. Sandy beaches in this area around 540 million years ago created this sandstone formation.
Bright Angel Shale - The water moved further inland, causing this area to be frequently underwater and covered with deposits of mud (which is where shale comes from).
Muav Limestone - The water got deeper and the area became part of the sea-floor proper leading to limestone deposits.
Following the Muav Limestone, the sea appears to have receded and the land was again above water. Little is left from this period.
Redwall Limestone - Around 363 million years ago, the sea moves in rapidly again and the area is once again part of a sea floor leading to limestone deposits.
Supai Group and Hermit Shale - This is actually a lot of smaller layers (a mix of shales, mudstones, and limestones) created as the sea came in and went out numerous times over a period of 30 million years.
Coconino Sandstone - The seas pulled back and this part of North America became part of a vast sand-dune filled desert (similar to North Africa). The Coconino Sandstone is the petrified remains of ancient sand dunes.
Toroweap Formation and Kaibab Limestone (top of canyon) - The sea came back and turned the area first into shallow mud flats (Toroweap) and then drowned it completely into a sea floor (Kaibab) about 240 million years ago.
One frequent related question... how can Grand Canyon rock layers be from the bottom of a sea when the canyon rim is at 6000+ feet elevation, did the water get that high? The answer is no... at the time that the sea floor deposits were created, this part of North America was much lower (ie: below sea level).