The rule itself reads.
Stop and check position of drawbridge, spring switch, derail, gates protecting railroad crossing, ensure the way is clear and drawbridge, spring switch, derails, or gates are in proper position and proceed at Restricted speed
The rule sounds simple enough, sort of splitting the difference between a Rule 292 Stop signal and a Rule 291 Stop and Proceed signal. However, to fully understand Stop and Check and the reasons for its use you have to place yourself in the context of the single line, train order based system of operation that predominated in much of North America up until the 1960's. Growing up in the Northeast with its heavily industrialized past it is easy to develop a rather bias view of what railroading should consist of. I.E. Main lines have 2 (or more) tracks, signaled with ABS and interlockings (manned or otherwise) are plentiful, especially at main line diamond crossings and movable bridges. Secondary tracks can be single and controlled by manual block or train orders, but its not such a big deal because those are the old agricultural lines that don't even exist any more. Maybe if a railroad was trying to pinch pennies that might employ something with Absolute Permissive Block with swing switched passing sidings and holdout signals, but that's more an interurban thing. This point of view would also apply in Europe.
Unfortunately this reality only existed where industrial and population conditions allowed for it as things like two track main lines and interlockings are big ticket items that railroads serving areas that consist mostly of empty land or farm fields simply could not afford. In these places the model was single track main lines with passing sidings and some bi-directional ABS if you were lucky. Interlockings were few and far between with diamond crossings and movable bridges getting no special pass on this. Oh, and trains dispatch themselves working with timetable and train order. For a system that did whatever it could to eliminate the need for full fledged interlockings, Rule 293 Stop and Check is to diamond crossings and movable bridges as spring switches and absolute automatic hold out signals are passing sidings.
Stop and Check plated signals are automatics in that there is no human that can push a button and set them to absolute Stop, yet they are attached to things that might often require an absolute stop like diamond crossings and movable bridges. However they can get away with this because what Stop and Check protects does not represent a decision point for the train. Instead of spending money to install an interlocking that must have routes set by a human and must require human intervention in case of a failure, Stop and Check allows train crews to inspect local conditions on their own and continue without external input.
Now the usefulness of Stop and Check is clear in the old Train Order days, but why would they appear on modern CTC lines? Well under early modern CTC schemes where Stop and Check is likely to appear there are several factors at play. First you'll still save money using Stop and Check than installing an interlocking. Second, the majority of railroads outside of the Northeast industrial belt did not adopt a Call-on aspect as standard in their CTC interlockings so if there was a problem affecting the ABS logic of an interlocking a signal could not be displayed even if the routing logic checked out. Passing such signals would require dispatcher intervention, which on a low density line isn't a huge problem, but the more absolute signals one installs, the greater the potential for disruption. Finally, simply fitting an old train order operation main line with CTC doesn't necessarily eliminate the old train order mentality. The line is still single track with short passing sidings. Fitting fully fledged interlockings in the space between these sidings only allows for dispatchers to screw up and create Mexican standoffs at the movable bridge or diamond crossing. Since routing decisions can only be made at passing sidings there is no reason to allow dispatchers to exercise control at intermediate points unless there is an explicit need for a holdout signal.
Alright then, I think this is a pretty good investigation of the context behind Stop and Check so let us look at a real life example located in Athens, Georgia where the CSX Abbeville (nee SAL) crosses the former Central Railroad of Georgia Athens branch crossed. Today the old CoG line is run by a shortline serving local industries north and south of the city. It sees nowhere near the level of traffic as the Abbeville Sub does and therefore there is no need for full time mediation of routes at the crossing. The crossing is also one block north of Fowler Junction passing siding and while a holdout would be appropriate here, it was not seen as necessary.
We begin looking north along the Abbeville Sub and one thing in our immediate favor is that for whatever reason these signals are not approach lit so unlike every other signal on this line we are treated to constant stream of block occupancy and direction of traffic information. Also in evidence is a solar powered rail greaser, and a call box that may or may not still be in operation. Keep in mind this is not an interlocking and as such has no station name associated with it. It's only reference in the employee timetable is on the diagram and there are no special instructions regarding a "railroad crossing at grade. So for train crews the only thing special about this location s that (C) plate.