I suspect that if you don't flush first the first shot you pull will be made with cool or cold water. The idea is to heat the brew head and to empty the cold or luke-warm water that is in the pipes, replacing it with properly tempered (ca. 94°C) water. You won't hurt the machine by not doing it, but you won't be getting a very good extraction with cooler water. In addition, you will be using "stale" water that was heated yesterday and sitting the pipes overnight, probably not the best conditions for good flavour.
Larger commercial and most so-called "prosumer" machines have systems that independently heat the brew head, but especially in the morning after turning on the machine it is a good idea to run some water through to make sure that fresh water from the heat exchanger or second boiler is available for the shot. With a smaller home machine it is all the more important.
talltom wrote:I have a Gaggia Classic. If I am using it on a daily basis, do I need to run some water through the grouphead every time I turn it on? If so, what happens if you don't do that? Presumably there is still water in the boiler from the last time you used it. I ask because I keep forgetting to do that when I turn it on, but it says in the instructions that you are supposed to.