"Single shear"/"double shear" refers to how a screw/bolt is loaded when the force is perpendicular to the axis of the fastener (when the fastener is loaded parallel to the axis, it is loaded "in tension.")
If a screw/bolt is loaded in shear, it's usually being used as a pivot, and there are other design considerations that should be applied as well (for instance, a threaded fastener should never be loaded in shear on the threads - it should be loaded in shear on the shank, or "grip.")
"Single shear" refers to the fact that there is a single plane of shear force through the fastener - an example would be a tie rod end stud. Even with the taper to locate the parts, there is a single shear plane - it exists between the tie rod end housing and the knuckle surface (typically considered to be even with the lower plane of the knuckle surface.)
"Double shear" would mean that there are two shear planes through the fastener, or that the total shear force is "split" into two locations on the fastener body. It's most common to see hitch pins loaded in double shear - a good example of this would be the cross pin for your trailer hitch. You know how you put the shank of the ball mount into the receiver, and then retain it with a large (~5/8") pin? That pin is loaded in "double shear" - one plane on either side of the ball mount shank.
Loading a fastener in "double shear" allows you to either not quite double the load on it, or to use a smaller fastener (since the load is split.) You'll still want to select for the shear load to be placed on the shank instead of the threads (where the available shear strength is rather lower!) While I like to leave a good safe margin for anything (without testing, shear strength can be estimated as being 75% of tensile strength, and tensile strengths for ISO and SAE fasteners are easy to find,) this still gives guidelines for not wandering too far into overkill.
Note that there is a fairly significant reduction in strength when loading a fastener in shear over the threads (due to reduced cross-sectional area.) I don't have it to hand, but I've been planning a "fastener primer" that will explain just how you can figure the reduction in strength due to threading. There is a similar reduction in strength when loading in tension - same reason. You use the minimum cross-sectional area at the thread root for strength calculations in tension, and you should be able to use the full nominal diameter in shear (unless you screwed up, and loaded it in shear across the threads...)