Consciousness -- that is, "phenomenal" consciousness, the stream of experience, subjective experience, "what-it's-like"-ness -- might be sparse, or it might be abundant. There might be lots of it, or there might be very little. This might be so along at least five different dimensions of analysis.
Entity sparseness vs. entity abundance. Consciousness might be sparse in the sense that few entities in the universe possess it, or it might be abundant in the sense that many entities in the universe possess it. Someone who thinks that consciousness is entity-abundant might think that insects are conscious, and snails, maybe earthworms -- all kinds of entities with sensory systems. They might also think that computers could soon have conscious experiences, if designed in the right way. At the extreme, they might accept panpsychism -- the view that every entity in the universe is conscious, even isolated hydrogen ions in outer space. In contrast, someone who thinks that consciousness is entity-sparse is much more conservative, seeing consciousness on Earth as limited, for example, only to cognitively sophisticated mammals and birds, or in the extreme only to adult human beings with sophisticated self-reflective powers.
State sparseness vs. state abundance. An entity who is conscious might be conscious all the time or only once in a while. Someone who thinks that consciousness is state abundant might think that even when we aren't in REM sleep we have dreams or dreamlike experiences or at least experiences of some sort. They might think that when we're driving absent-mindedly and can't remember a thing, we don't really blank out completely. In contrast, someone who thinks that consciousness is state sparse would hold that we are often not conscious at all. Consciousness might disappear entirely during long periods of dreamless sleep, or during habitual activity, or maybe during "flow" states of skillful activity. Someone who holds to extreme state sparseness might say that we are almost never actually phenomenally conscious, except in rare moments of explicit self-reflection.
Modality sparseness vs. modality abundance. An entity who is currently state conscious might be conscious in lots of modalities at once or in only one or few modalities at a time. For example, a minute ago, as you were reading the previous paragraph, did you have visual experience of the computer screen? Did you also have auditory experience of the hum of the fan in your room (to which I assume you weren't attending)? Did you have tactile experience of your feet in your shoes? Did you hear the words of that paragraph in inner speech? Did you have relevant visual imagery? Were you also simultaneously having emotional experience, a lingering feeling of hunger, etc., etc.? Someone who accepts modality abundance thinks that we have many types or modalities of experience ongoing most of the time when we are conscious. In contrast, someone who accepts modality sparseness thinks that we have only one or a few modalities of experience at any one time -- for example, no experience at all of the feeling of your feet in your shoes when your attention is elsewhere.
Modality width. Within a modality that is currently conscious in an entity at a time, the stream of experience might be broad or it might be narrow. Consider visual experience as you are reading. Do you have visual experience only of a few degrees of visual arc, whatever is near the center of your attention? Or do you have visual experience all the way out to the edge, including the rim of your computer screen, the rims of your glasses, the tip of your nose, almost 180 degrees of arc? Or somewhere in between -- maybe the whole computer screen and its rim, but little beyond that? Someone with a sparse view about visual modal width thinks that visual experience is usually (maybe until you think to attend to the periphery) only of a few degrees of arc. Someone with an abundant view might think that we basically experience the full 180 degrees of the visual field all the time when we have any visual experience at all. Analogous issues arise for other modalities. Do you have auditory experience only of the conversation to which you are attending, or also of the background noise? Is your visual imagery sketchily minimal or full of detail? Is your emotional experience a minimal valence and label or is it a very specifically embodied feeling?
Property sparseness vs. property abundance. Consider visual experience again. You are looking at a tree. According to one view, all you visually experience are low-level properties like color, shape, and orientation. You know it's a tree, but the "treeness" of it isn't part of your visual experience. (Maybe you have a cognitive experience of thinking "tree!" but that's a different modality.) According to another view, your visual experience is not just of simple low-level properties but instead of a wealth of properties. It's part of your visual experience, for example, that it's a tree, and that it looks ancient, and that it invites climbing, and that the leaves look about ready to fall.
Philosophers and consciousness scientists have recently been arguing in all kinds of interesting ways about various of these issues in isolation, but I can't recall seeing a good structuring of the landscape of options here which both captures the many different mix-and-match possibilities here, while also recognizing that all of the "abundant" views have something in common (consciousness is widespread and multifarious; it's easy to generate lots of types of it) and all of the "sparse" views have something in common (consciousness is rare and limited in its forms).