A feature class is a table with geometry; it is pure data. A lyr file, or a layer inside a map, is just a pointer to data, usually one feature class (but there are group layers). Layers can be saved and shared to save time in building maps or repointing maps to data (feature classes) when the data has moved, and to enforce consistency and quality. A layer can store every property that can be accessed from the Properties dialog in ArcMap, including fields shown, field aliases, symbology, labeling rules, default display field, time handling rules, field order, popups, and selections.
A feature class may be updated; this will automatically be reflected in maps and lyr files accessed after the update. But if the lyr or mxd needs to change, e.g. because the data's fields and location have changed enough that the layer won't draw, users will have to bring in an updated, corrected layer (or try to fix it themselves). When you first add a lyr to your map, you took a snapshot in time; the map will not know if a layer's properties need to be updated...you may see a red exclamation point or get a drawing error.
In my shop, we tell everyone to add data from lyr files because it keeps everyone looking at the best data. I maintain a library of about 150 lyr files.