Okay so what you're generally looking at is the past 40 days and the next predicted 15 days. The green line represents the model. The yellow lines are ensembles. Dark lines are the prior 40 days. The shaded grey areas encompass the area of ensembles and show their general trend.
I'm not an expert on this by any stretch. I just watch it. The short of it is that the MJO Phase is based on where upward motion is occurring in the Pacific or Indian Oceans - which moves west to east (propagates) across the equatorial regions. It's a measure of intraseason variability of the atmosphere in the tropics. Some years this is a very strong weather signal, 2020 has been one of those years so far. Some years it isn't and doesn't really make it across the Pacific or is limited in scope and effect. Downstream implications for North America can be deduced from the way weather behaves farther west because of the direction of earth's rotation. Think about the Pacific basin and weather. What happens there is often an indicator on what's to come here. You can use things like whether there is a mean trough west of Hawaii, east of Hawaii, whether thunderstorms are firing off in the west or east Indian Ocean, WPAC hurricanes recurving or plowing westward or westnorthwestward, etc. <-- or in other words, things happening west can tell us what's going to happen farther east.
There are 8 phases of the MJO. These phases have corresponding places where tropical cyclones (and certainly other weather) are most likely to form, be, behave, etc. based on given phases. For Phases 8, 1, 2 and 3, the western Atlantic is in a riper stage of upward motion. Phase 1 also favors upward motion in the EPAC. Phases 2 and 3 are so-called hyper phases for much of the big islands and the USA.
To answer your question as to what they are showing, most of them move from Phase 5 to Phase 1-ish over the next 2 weeks. Some curve down toward Phases 2 and 3. The circle in the middle is a more neutral indicator. MJO can still be sort of in Phase "x" but generally there is a weak signal when it's there. If/when a line gets way to the outer edge of the graph (the square outline), things tend to be super-amplified where things amplify in that particular phase.
Best place to start is the NCEP site where I got the images from. You scroll over the model names and it will display the phase plots. There are sites that show specifically model what happens in a particular phase. After this post, I'll dig one up.
https://www.cpc.ncep.noaa.gov/products/ ... r_wh.shtml
I'll be sinking into that ....