Judges 7:2: The Lord said to Gideon, “You have too many men. I cannot deliver Midian into their hands, or Israel would boast against me, ‘My own strength has saved me.’

God's purpose in this passage is to defeat Midian in such a way that Israel will have no grounds for boasting. He deliberately thinned out the army so that it was so tiny that there would be no way that Israel could say that its strength gave it victory.

Judges 7:4: But the Lord said to Gideon, “There are still too many men. Take them down to the water, and I will thin them out for you there. If I say, ‘This one shall go with you,’ he shall go; but if I say, ‘This one shall not go with you,’ he shall not go.”

So then when God tells Gideon to take his men down to the water he says he will direct Gideon about who should be kept and who should be sent home. Again, the concern is the number of men, not their quality or training.

So I have to disagree with all the other answers saying that those who lapped water were somehow more alert, professional, virtuous, or otherwise better soldiers. Nothing in the text indicates that God picked them because they were better soldiers than the others. And indeed, in the coming battle super soldiers were not needed, because it was not a conventional fight.

I think verse 4 indicates that it was a largely arbitrary distinction. God said that there were too many men, and selecting those who lapped thinned out the army how God wanted. If the majority of the 10,000 soldiers had been more alert and lapped the water, then I think God would have picked the 300 who knelt, in order to remove any opportunity for boasting.