Since someone asked below I figured I'd expand on this. Here, I pulled the number of flights per day of week for the whole year 2018 by month:
That's a lot of numbers to look at, but the summary looks like this: In total, there are around 8.6 million flights that either happened or will happen in 2018. The daily average is about 23,800. For each day of the week the averages are below:
So comparing these numbers shows us that (at least approximately) Tuesday, Wednesday, and Sunday are about average. Monday, Thursday, and Friday are, respectively, 1%, 2.5%, and 4% above average. Saturday, meanwhile, is almost 8% below average. Hence, it seems pretty clear that Saturday is the day with the fewest flights at the airport.
However, the same caveat from the original answer still applies: This doesn't necessarily mean that Saturday is less busy than the other days. To know that we would need to know the average load factor of airlines around the world. However, specific values of that number are not shared for competitive reasons so it comes down to my personal experience that indicates that Saturdays also have a significantly lower load factor than other days of the week. Lower load factor and fewer flights together should make that the least busy day at the airport.
I just pulled the industry data for the month of October 2018 to check this out for you. Here are the world-wide totals for flights this month by day of week:
From this, you could conclude that Saturday is the least busy day at the airport, followed by Sunday and then Tuesday. Of course, the number of flights is not necessarily correlated with the busiest days at the airport because those flights may not be full. From my experience working at a major US airline, we expect, based on our historical data, Tuesday, Wednesday, and Saturday to be our days with the lightest loads.
This explains why prices are cheaper those days. Airlines are trying to entice people to fly on Tuesday (for example) because our flights normally aren't as full that day. However, we still want to operate as close to a full schedule as possible because there is still enough demand. Finding the right balance is key to running a successful airline.
Source: Diio Mi, an airline industry data source.