Fair enough, obviously these symmetries were trying to tell us something about the composition of hadrons. What? Well, needless to say, Gell-Mann did not immediately come up with a simple nuts-and-bolts assembly manual; instead, they developed an abstract mathematical description called analogous to the description of spin for electrons, . [If you're interested, the acronym stands for Simple Unitary group of order 2 or 3.] I won't attempt to elaborate, but you can see why something like this was needed - as for the component of spin, the projections of the three operators along God-only-knows what axes in God-only-knows what dimensions cannot have a continuum of possible values but only a fixed number of discrete or quantized values. What is actually refers to is totally unknown. Or, more properly, it refers to just what it says; if that means nothing to us, well, that's just because our empirical personal experience of the space of is so limited that we don't relate to it very well. What do "normal" space and time actually refer to?
Anyway, someone inevitably formulated a simpler instruction manual for assembling hadrons. This was to give the requisite properties to three (there are more now, but hold off on that) really fundamental component particles called "quarks." All mesons are composed of a quark-antiquark pair whereas baryons are composed of three quarks held together by a "superstrong" force mediated by a new type of intermediary called "gluons" (g) [more cuteness, but who can argue...].
Table:
The known (or suspected) "generations" of quarks.
Figure:
Upper left: the three lowest-mass quarks.
Lower left: the corresponding antiquarks.
Right: the spin- baryons.