It is to make up for the 11 minute creep that years divisible by 4 are not leap years if they are divisible by 100 unless they are divisible by 400. This system is also not perfect and introduces some error that could result in the year 4000 not being leap year.
As for the relevance of 11 minutes, it is substantial. The GPS navigation systems used almost everywhere today is based on the measurement of time to the millionths of a second. Though our saying that one year has 365 days and another 366 year may not affect the grand scheme of things for many it is very relevant. Some of the things that I imagine could happen that would affect everyone would be a shut down of stock exchanges, flight delays, major train crashes, people having to put on their television sets at different times every week to catch the same show and the alike. We are now living in such a complex World that that these small things that most would consider inconsequential can affect everyone's life.