> This means the atomic clock is behind the solar clock by 37 seconds?

If anything, it's the other way around.

A UTC day is defined as exactly 86400 SI seconds. But an actual mean solar day is a few milliseconds longer (although the difference is not constant due to irregularities in the Earth's rotation--but the average difference is expected to slowly increase over time). SI seconds are counted by atomic clocks, so UTC advances its day by one every 86400 atomic clock seconds.

But a solar clock that advances its day by one every time the mean sun reaches noon (it has to be the mean sun because the rate at which the actual sun moves across the sky varies over the course of a year, we need to look at the average) will advance its day a few milliseconds later than UTC does. Or, to put it another way, each time period that the solar clock says is exactly 86400 seconds, is a few milliseconds longer according to the atomic clock.

As this happens day after day, the difference accumulates, and when it gets close to being a full second, a leap second gets inserted into UTC, so that one of its days is 86401 seconds long instead of 86400. The reason for this is that UTC is not just counting atomic clock time; it also has to stay in sync with where the sun is in the sky since so many human activities are tied to that. And we humans have defined "in sync with the sun" to be "within a second of the average sun". In other words, we want UTC noon to be within a second of mean solar noon on the prime meridian.

So the 37 seconds is how far mean solar noon would be behind UTC noon, if we didn't use leap seconds--at UTC noon, the mean sun would be 37 seconds short of actually crossing the prime meridian in the sky.