We did not skip the leap day (February 29) in 2000, because it is divisible by 400. The last time we did skip the leap day was in 1900, which meant that people born on February 29, 1896 did not have their first birthday until age 8 (in 1904), and had their birthday next falling on the same day of week (Saturday) at age 12 (in 1908) rather than at age 28 (in 1924). The next skipped leap year will be the year 2100. This means that while the years 1904, 1932, 1960, 1988, 2016, 2044, and 2072 all had or will have March 1 on Tuesdays, the year 2100 will have March 1 on a Monday.
How will this affect us? Imagine that you had went to sleep on Sunday, February 28, 2100, and then woke up the following day looking at the calendar and saw that the 29th of February did not appear. Would you be surprised that the year 2100 skips the leap day for the first time since 1900? We will also skip leap days in 2200 and 2300, of course, but not in 2400, the next year after 1600 and 2000 to be divisible by 400.