If you look at a century-long graph of ocean temperature, you don't see a smooth rise but a staircase. Two big steps upward: one around 1925, the other around 1987. Between the steps, the temperature wandered up and down a bit, like waves on the sea, but after each step the average level stayed higher.
Why is that? Scientists took two datasets of sea surface temperature and tried to explain them with a simple model. The model included only two things: known oscillations (El Niño in the tropics and a slow oscillation in the North Pacific) and two sharp jumps. It turned out that this was enough to describe almost all the changes over the century. No smooth trend was needed.
Previously, it was unclear why warming proceeded unevenly: sometimes fast, sometimes stalled. Now we see that it's not random but two major transitions. And if such a transition happens again, we'll be able to spot it, because we know what it looks like.
The 1976/77 shift, often considered the largest regime shift of the twentieth century, isn't recognized as such in this study: it's almost entirely explained by natural El Niño variability. The 1987/88 shift, in contrast, stands out precisely because it can't be reduced to known oscillations.