I have always struggled to get my head around the MJO and ENSO until I found this allegory/description. I hope it helps similarly MJO challenged folk as myself!
Imagine ENSO as a person riding a stationary exercise bike in the middle of a stage all day long. His unchanging location is associated with the persistent changes in tropical rainfall and winds that we have previously described as being linked to ENSO. Now imagine another bike rider entering the stage on the left and pedaling slowly across the stage, passing the stationary bike (ENSO), and exiting the stage at the right. This bike rider we will call the MJO and he/she may cross the stage from left to right several times during the show.
So, unlike ENSO, which is stationary, the MJO is an eastward moving disturbance of clouds, rainfall, winds, and pressure that traverses the planet in the tropics and returns to its initial starting point in 30 to 60 days, on average.