Merriam-Webster defines the term 'bryology' as "a branch of botany that deals with bryophytes" which is really helpful for anyone who has no clue what either of those words mean. In simple man's terms, a bryophyte is a moss, liverwort, or hornwort. Mosses are the most commonly known of the three (and in my personal opinion) the most exciting. Bryophta, which is the taxonomical division containing all bryophytes, is best described as flowerless, seedless plants with nonvascular tissue. Okay, we're getting to the point where this is easier to understand, so let's break down this definition.
Flowerless
This is easily one of the most defining features of a bryophyte, and one of the most discernable when looking for them. It's as simple as if the plant has flowers growing from it, it cannot be a bryophyte. The horticulture industry loves to give misleading information when it comes to labeling plants, For example, Sagina Subulata (Irish Moss) is branded as a moss, but is not a moss at all! Irish Moss is a low growing, evergreen perennial that produces little white flowers and is commonly used for groundcover and turf.
Seedless
Bryophytes do not have seeds, unlike many other plants that you know, they do not pollinate and drop seeds to carry on their lineage. I can already hear you asking yourself "Well if bryophytes don't have seeds, how do they reproduce?" I'm glad you asked! Bryophytes reproduce via spores, which you may know from fungi and ferns. In the bryophyte lifecycle, when the sperm fertilizes the egg, the gametophyte will produce a stalk called a sporophyte- which has a pod on the end called a capsule, that holds the spores until they are released by an external force. This could be a deer walking over the moss, a rain storm, or even just the wind. One of my favorite things to do out in the field is find mature sporophytes and brush my hand over them, watching the puffs of orange dust dissipate into the air, on a journey to create new moss.
Although this is not the only was that bryophytes can reproduce. Bryophytes have the ability to reproduce asexually and spread through gemmae, which is essentially just a fragment of the plant that can develop new growth, and in turn, a new plant. In mosses, this can be part of the stem or one of the leaves, even as little as a single cell can produce a new plant. In liverworts, the gemmae are haploid tissue produced inside of gemma cups.
Nonvascular Tissue
When you think of a plant, you imagine a root system in the ground sucking up nutrients and providing the plant with the water it needs to undergo photosynthesis. Bryophytes don't do that, because they lack the vascular tissue (phloem and xylem) needed to transport nutrients throughout the plant, in fact, they don't have root systems at all! Instead, they obtain water and nutrients via osmosis, which if you remember back to your high school biology class, is the net movement of molecules through a semi-permeable membrane. This means that they suck all of the water and nutrients they need through the surface or leaves of the plant. Bryophytes are remarkably well at holding water too, which is why they are considered the sponges of the forest, the water is held between the leaves of the plant, allowing it to stay damp through periods of extended drought. Some species of moss can hold up to 17x their dry weight in water! Instead of roots controlling the uptake of nutrients, bryophytes have appendages called rhizoids, which act as an anchor for the plant. These rhizoids exist solely to attach the plant to a surface, which is why you can see moss growing where other plants cannot (I.e. on the sides of trees, or on top of a boulder).
Conclusion
Now that we have dissected the defining features of bryophytes, I hope that it makes it a little easier to understand why these plants are so amazing, they have gone down a completely different evolutionary path than most vascular plants, and while they may not grow impressive flowers, produce tasty seeds, or have the complex structures as other plants, they are just as interesting in their own way.