A pick-off mirror is a mirror that takes light from the telescope's common optical path and directs the incoming light to a specific instrument or sensor. There are two use-cases for them (at least as far as I'm aware):
- to redirect all the light to an instrument
- to temporarily redirect part of the light to a sensor for e.g. calibration purposes
For this, pick-off mirrors are typically movable and they can be inserted into or removed from the optical path.
For the first use case: it's basically a way to multiplex incoming light. A telescope has only one focal point, but typically many instruments, so you can't have them all observe at the same time. Pick-off mirrors redirect the light to the instrument you want to use.
When a ground-based telescope switches between cameras, sometimes the instrument is physically taken off the telescope, and a new one is installed during the daytime when the telescope is not in use. If the other instrument is already on the telescope, mechanisms are in place to move part of the telescope’s optics (known as a pick-off mirror) into the field of view.
(from: NASA blogpost)
While JWST doesn't use moveable pick-off mirrors for this use case (see above blog post and below), it's not that space telescopes don't use them at all. E.g. Hubble uses pick-off mirrors too.
The second use case is to direct only a portion of the incoming light to a different sensor. This can be in an instrument that consists of multiple sensors, but also for calibration purposes. For example: the ESO Extremely Large Telescope (ELT) uses small pick-off mirrors to redirect part of the incoming light to a guide star tracker that takes measurements for the purpose of wavefront corrections. These observations must be made in parallel to the science observations, so that the science data can be corrected in post processing. (ELT also uses a pick-off mirror to direct light to the science instruments that are off-axis, but in that context the mirror is just called M6.)
JWST does not have movable pick-off mirrors (see blog post, but instead all the instruments are in the focal plane. However, JWST nomenclature still uses "pick-off mirror" for the first mirror in the instrument-specific optical path that takes light from the focal plane to the instrument (as illustrated in the question post).
There are 4 instruments that each have their own pick-off mirror:
Also the FGS (Fine Guidance Sensor; not really an instrument) has one pick-off mirror.
A total of 6 pick-off mirrors.
However, it is again noted that all "pick-off mirror" in JWST are fixed mirrors (in the sense that you cannot move them out of the optical path) and in some cases they embody multiple functions (e.g. the NIRISS pick-off mirror has occulters engraved).
As to what to look like: they all look different. Here is a photo of one of the NIRspec pick-off mirrors.