Dorothy inherited the Elements after she caused East's death. The gauntlets transferred themselves to her and disappeared shortly after, leaving her perplexed.
Most obvious power the Elements give to their bearer is the control over weather - this can be attributed to the control over four elements: earth, wind, water and fire. Dorothy attempted to use the Elements in East's castle, when she tried to calm unsettled weather. Without the Elements, she would not be able to cross the lake and the sharpness.
When East was wearing the gauntlets, she exhibited the power of telekinesis. It's not clear if that was connected to the Elements or a power of Cardinal Witch.
According to Sullivan, the Elements are to be taught and he expected Mistress East to teach her acolyte how to use them.
- The gauntlets are the show's equivalent to 1939 movie's ruby slippers. Which, on the other hand, are based on silver slippers from the books. The red color was MGM's idea to fully take advantage of the marvels of technicolor.