flavor quantum numbers
Particles wear a set of permanent labels — little tags that say what they are and that nature keeps track of in reactions. Some labels you have met: electric charge, baryon number, lepton number. Flavor quantum numbers are another family of such tags, one for each of the heavier kinds of quark, used to keep count of how many of that quark a particle contains.
There are six kinds of quark, called flavors: up, down, strange, charm, bottom, and top. For the four heavier ones (strange, charm, bottom, top) physicists assign a quantum number — strangeness, charm, bottomness, and topness — that simply counts how many of that quark, minus its antiquarks, a particle holds. A particle containing one charm quark has charm +1; its antiparticle has charm -1; a particle with no charm quarks has charm 0. The crucial rule is the same one we saw for strangeness: the strong force and electromagnetism conserve every flavor number exactly, because they never change one quark flavor into another. Only the weak force can change flavor, turning, say, a charm quark into a strange quark.
These labels are the everyday accounting tools of hadron physics. They tell you instantly whether a reaction can proceed through the fast strong force (flavors balance) or must wait for the slow weak force (a flavor must change), which in turn governs how long a particle lives. The pattern repeats for each new quark: strangeness was found first in the 1950s, charm was confirmed in 1974 with the discovery of the J/psi particle, and bottom and top followed. Each new flavor quantum number marked the discovery of a new layer of matter.
A D meson contains a charm quark, so it has charm +1. The strong force cannot make it decay, because that would require destroying the lone charm quark and changing flavor. Only the weak force can do that, turning the charm into a strange or down quark — which is why D mesons live long enough to leave a measurable track.
A charmed particle can only decay by the flavor-changing weak force.
Flavor quantum numbers are conserved by the strong and electromagnetic forces but routinely violated by the weak force; that is precisely why heavy-quark particles decay. The top quark is so heavy it decays before it can even bind into a hadron, so it has no settled hadron spectroscopy of its own.