Microphonic noise results from vacuum tubes picking up mechanical vibrations and modulating the signal.
A vacuum tube is an electro-mechanical device. The electric characteristic of a tube heavily depends on the mechanical gap between the internal electrodes. Especially the grid and cathode.
The grid of a vacuum tube is a very thin wire wound around two long posts like a spring. As you can imagine, this spring will pick up vibration easily, which modulates the signal passing through the vacuum tube.
In that sense, a vacuum tube works like a very Lo-Fi (i.e., crappy) microphone. Hence we call this phenomenon "microphonic noise."
Because of how vacuum tube is constructed, all vacuum tubes are microphonic to some extent.
Of course, microphonic noise is not desirable. So vacuum tubes are designed to reduce microphonic noise by reducing vibration transmission and stopping electrodes from shaking.
Even then, some tubes are inherently more susceptible to microphonic noise than others. For example, it's impossible to eliminate microphonic noise from small tubes with larger plate boxes such as 12BH7.
On the other hand, current production 12AX7 or 6DJ8 tubes have minimal microphonic noise.
A tube may be more microphonic at a particular frequency. In high-gain applications such as phono amps or high-volume guitar amps, this can cause feedback issues. In such tubes, the glass tube and the internals resonate particularly well at a specific frequency. You can put an O-ring on the tube, or as Mesa does, wrap the tube in heat-shrink tubing. The O-ring or heat-shrink tubing changes the tube's resonance and can eliminate the howling feedback.
A tube may become more microphonic as it ages. As a tube is thermally cycled from use, internal components might shift slightly, making it more prone to resonance. Tubes becoming microphonic with use is uncommon, though. We have only seen a handful of such tubes.
At Tubes For Amps, we offer low-noise options where low-microphonic tubes are needed. The only way to know whether a tube is microphonic is to listen to it. On tubes that offer low-noise options, we listen to every tube and set aside those deemed low noise. As you can imagine, it takes time and expertise to do this right.
Some amps are far more prone to microphonic noise than others, so it's best to get tubes screened for low noise if you own such amps.