D-branes are a special and important subset of branes defined by the condition that fundamental strings can end on the D-branes. This is literally the technical definition of D-branes, and it turns out that this simple fact determines all of the properties of D-branes.

Perturbatively, fundamental strings are more fundamental than branes or any other objects. In that old-fashioned description, D-branes are "solitons"—configurations  of classical fields that arise from the closed strings. They are analogous to magnetic monopoles, which may also be written as classical configurations of the "more fundamental fields" in field theory. In a similar way, D-brane masses diverge for. Non-perturbatively, D-branes and other branes are equally fundamental as strings. In fact, when sent to infinity, some D-branes may become the lightest objects—usually strings of a dual (S-dual) theory. When we include very strongly coupled regimes (high values of the string coupling constant), there is a brane democracy.

Back to the perturbative realm. The condition that open strings can end on D-branes and nowhere else means that there exists a particular spectrum of open strings stretched between such D-branes. By quantifying these open strings, we obtain all the fields that propagate along (and in between) such D-branes. The usual methods (world sheets of all topologies, now allowing boundaries) allow us to calculate all the interactions of these modes, too.

So yes, D-branes also vibrate. But because their tension goes to infinity, you need even more energy to excite these vibrations than for strings. The quanta of these vibrations are particles identified with open strings that move along these D-branes but are stuck on them. The insight that the D-branes are dynamical and may vibrate, and the insight that they carry Ramond-Ramond charges (generalizations of the electromagnetic field one obtains from superstrings whose all RNS fermionic fields are periodic on the world sheet) were the main insights of Joe Polchinski in 1995 that made D-branes essential players and helped to drive the second superstring revolution.

Other branes typically have qualitatively similar properties as D-branes, but one must use different methods to determine these properties.

When we quantize a D-brane, we find open string states, which are scalars corresponding to the transverse positions. It follows that D-branes may be embedded into spacetime in any way. The shape oscillates according to a generalized wave equation again. Also, all D-branes carry electromagnetic fields in them. These fields are excited by the endpoints of the open strings that behave as quarks (or antiquarks). For a stack of coincident bars, the gauge group gets promoted to The electric flux inside the D-branes may be viewed as a "fuzzy" continuation of the open strings that completes them into "de facto closed strings."

Those fields have superpartners in the case of the supersymmetric D-branes, which are stable and the most important ones, of course. D-branes may collide and interact much like all other objects.

The most appropriate interaction that allows the open strings to "disconnect" from D-branes is the event in which two end points (of the opposite type, if the open strings are oriented) collide. Much like a quark and an antiquark, these two endpoints may annihilate. In this process, an open string may become a closed string, which may escape from the D-brane. The same local process of "annihilation of the endpoints" may also merge two open strings into one. Such interactions are the elementary explanations of all the interactions between the fields produced by the open strings—for example, between the transverse scalars and the electromagnetic fields within the D-brane.

Aside from that, some branes may also be open branes and end on another kind of brane. The latter brane always includes some generalized electromagnetic fields that are sourced by the endpoints, end curves, or whatever the p-1 dimensional geometry of the boundary of the former brane is.