What you have is three conductors in a sheath with a female end that is not common for RV use. It could work if the male end is either a 30 amp RV three prong, the wire is of sufficient size to carry 30 amps, and the three conductors attached to the ends are connected correctly. It could also work at lower amperage if you have a standard 120v male end but you will be limited to connecting to 20 amp service. It would really help if you posted a picture of the male end and a pic of the text/numbers on the jacket of the cable.
To test, you would set your multimeter to "continuity" or "resistance". Place one probe in each female opening and the other probe on the corresponding male end of the cord. All three should have individual continuity and zero resistance. None should have continuity to another. You also want to check that the round pin of the male end is the prong used for ground. I believe you might have inadvertently found the latter out if you plugged the cord into a receptacle. If the round pin was not ground, there would have been a short to earth and a circuit breaker would have tripped.
We could definitely use some more information including the wire size, if your trailer end has the matching male socket, and what the male end of the cord is.