Static friction is what opposes movement between two surfaces that are static next to each other and kinetic friction is what slows down movement between two surfaces. Static friction is always >= kinetic friction.
This is explained very well in here (the top picture says it all): http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html
Think about how when you start your car from a standstill you need to be careful about your clutch release but when the car moves even the tiniest bit you can even start in the second gear if you want.
So, the engine car's wheels get kinetic friction (because they're rolling) and the other cars' wheels (which are stopped) are blocked by static friction. When you have slack and you move one car at a time you only need to beat the static friction of one car at a time. Even if the difference is 10%, if you have 10 cars and it starts to add up. I'm not saying slack is required for starting the train, just that there is an increased difficulty in doing so without slack.