There are different types of lag in Warcraft, different types are caused by different things in the chain (client, connection, server). The game is only as strong as the weakest link so you could have the best machine in the world, they could have all the server farms they want, but if you're playing over a dial-up, you are going to lag!
With the minimum spec you will find that the screen does not refresh fast enough. But your character will still be active in the virtual world - so if your computer lags when you're in a battle, by the time it catches up you will probably be dead. Similarly, if your machine lags when you are running, it is likely that you'll keep running while your machine catches up - you can spend an amusing 10 minutes in Ironforge watching people walk into the trench outside the auction house because they are suffering lag! :evil:
I suggest you look round the WoW support forums at
www.wow-europe.com - the tech support forum has some things to try to reduce lag.
But the bottom line is, lag will spoil your game because it makes battles unplayable, and most of WoW is battles!