The various pebbles larger than their surrounding rock (matrix) are all called clasts. Clasts can be quite small or very large - the current clast size record for our SMS drill hole stands at 36.08cm. That clast was so big that it looked like another thick layer of sediment going all the way across the core. We only get a little section of one that large - we don't really know what shape the entire clast might have been, no way to tell if we went through it the long way or only clipped a short side. Officially, any grain larger than 2mm is a clast.
There are clasts that have familiar shapes which the night crew sometimes names - like Groucho Marx's moustache or Sponge-Bob Square Clast. Some are beautiful marbles or granites that would make lovely jewelry. Some clasts are wildly colored - I've seen bright blues, greens, oranges, purples, reds, and yellows.
There may only be a few clasts in a section of core, or there may be so many that the section of core is mostly clast (some of these look like very fancy granite countertop or tile). Every clast in every meter of core is meticulously logged and described. Over 23,000 clasts so far!
Whether a clast is striped, plain, speckled, weathered, full of holes filled in with other minerals, in layers, or solo, it is an important piece of information about the environment at the time it was deposited and possibly earlier. For example, we can get very precise age dates for volcanic clasts as well as a history of volcanic activity in the area.
Clasts usually have travelled some distance before they got included in the rock where we found them. By tracking back to the parent rock layer where the clasts originated, we can learn about how drainage networks in the area worked at the time of deposition. Here in Antarctica, glaciers form the network but in most of the rest of the world, rivers and streams perform that function.
We might also learn about mountain building uplift of earth's crust. When the crust rises over time, mountains are created when some of the material erodes away and leaves only sections of the original rock. Those eroded bits are carried away and many are incorporated in other rock far away from their source. The further towards the top of the mountains a layer is, the more of that type of rock has been eroded and gone somewhere else. Look at the picture of the Trans Antarctic Mountains below and follow the layers across. You should be able to see that the layers towards the top have more material missing than the lower layers.
Find a bare patch of ground outdoors, preferably not in human imported sediments (i.e. a sandbox) and look at all the rocks and pebbles you can find there. Are they similar to one another? Are they similar to other rocks in the area? How many different kinds of rocks can you find? Someday, these pebbles might become clasts in a new layer of rock starting right in front of you!