It simply means testing of the enduring capability of the software product. "Endurance Testing" is done to examine the software's competency to perform consistently and accurately, over a longer period of time, along with the continuous increment in a load.
Also known by the name of soak testing, endurance testing is a type of non-functional testing that seeks to assess the efficiency and behaviour of the software under constantly increasing load, for a long duration. This type of testing guarantees the flexibility of the software product to function, continuously, without any deviation in performance, over an extended period.