The earth rotates like a top, and it also orbits the sun. If we went “up” from the North pole and looked down on our solar system, it would be orbiting the sun counter-clockwise and also spinning counter-clockwise.
If the Earth didn’t rotate at all, then the sun would still rise and set, but it’d go backwards, rising in the West and setting in the East, and a day would be a year long — six months of light, six months of darkness. So it’s like there’s one backwards-day built in, just because the Earth goes around the sun.
It’s easiest to visualize by literally just making a fist with one hand and calling it the sun, and using the finger on your other hand and making it go around the sun. If you lived on the fingernail side, it’d spend six months in darkness, but as it got around to the other side of the sun (your fist), then it’d be in daylight for six months.
So our days are (on average) 24 hours even though it only takes 23 hours and 56 minutes to rotate. That 4 minutes of extra time to complete a day is to counteract that built-in backwards day caused by Earth going around the sun. And that’s why extra 4 minutes a day every day for a whole year roughly equals that one backwards-day’s worth of time.
Leap years aren’t really related… They exist because the time it takes Earth to make one orbit isn’t an integer-number of days. It’s not 365 days — it’s actually about 365.2422 days. That’s very close to 364.25 days, so adding an extra day to the calendar every 4 years keeps us roughly in line with the actual length of a year. But it’s still not quite right, so we skip a leap-year every 100 years, which brings it down to 365.24 days per year on average, which is closer. But that’s not quite right, so we add a leap year every 400 years, which brings us up to 365.2425 days, which is *very* close to 364.2422 days. Theoretically if we keep the calendar for long enough, it’ll still drift, and maybe we have to remove a leap year once every three thousand years to keep it even closer.
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EDIT:
Incidentally, Venus is kind of in that “not rotating at all, just orbiting” situation. Not perfectly — it does rotate, albeit the wrong direction. So a day on Venus would be about six (Venusian) months long.
Mercury is somewhat similar, completing 3 rotations for every 2 orbits of the sun. That means a day on Mercury is longer than a year on Mercury… every 2 mercury-years, it makes 3 rotations, but has two backwards-days to cancel out from orbiting the sun, so a mercury-day ends up about 2 mercury-years long.
Checking Wikipedia, a mercury-year is 88 earth-days long, mercury-days are 176 earth-days long. So you could literally outrun a sunrise (ignoring the part where there’s nothing to breathe)
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