Excuse me means the same for dogs as it does when you say it people. It's a polite way to ask someone to move. This is one of my favorite and probably most used commands. Every time I use it in public, though, any person within earshot assumes I am speaking to them.
Relationship based training philosophy
The difficulty is in explaining how to teach Excuse Me. It's not a step-by-step process like teaching Sit. It's something you incorporate into everyday life. It's worth making the effort, however, because this command is so handy. Not only does it keep you from tripping over dogs when you're walking through your home, it also helps you to "move" them when they're in a place you'd rather they weren't, such as in front of the t.v. So, I will try.
If your dog gets in front of you while you are walking, do not change your course. Say "excuse me" and gently move them out of your way with your leg as you walk. Think of it as the way you would gently push your spouse out of the way if you wanted to get by. You give a little push, and they move the rest of the way on their own. That last part is important, so I'll say it again. You give the nudge in the right direction, and they move the rest of the way on their own. If you do it for them, they won't learn as quickly because "excuse me" will mean that you are going to move them. You want "excuse me" to mean that they are to move themselves.
If your dog is sitting or lying down in your path, do not step over him. Stop in front of him, and say "excuse me". Sometimes, just looking at them is enough to get them moving. If not, give a little encouragement - whatever gentle way you can think of to get your dog to move himself. Again, the idea is to just give him a nudge in the right direction and let him do it on his own.
That is all there is to it. Be consistent in using the command "excuse me" everytime you need your dog to move in order to help him learn it faster. If you're trying to open a door, and he is in the way, "excuse me". If you're trying to watch t.v., and he is blocking your view, "excuse me". Anytime you want your dog to move from the spot he is in, "excuse me".
Oh, and don't forget to say Thank You!