A no-hitter is when a team gets zero successful hits - meaning that they hit the ball in-bounds and then made it to first base.
If you're not familiar with how strikes/balls work, a strike is counted for each time the batter swings and misses, swings and hits a foul ball (unless that would be the third strike), or doesn't swing but lets the ball pass through the "strike zone". A ball is counted when the ball misses the strike zone and the batter doesn't swing.
If you get three strikes, you're out. Four balls, however, grants you a walk, which lets you advance to first base for free. This means that it's possible to score points without actually hitting the ball.
A ground out is when a fielder gets the ball and throws it to base before the batter can make it, which means that he's out. I'm not sure why it was brought up in this context, since it's definitely not how you score points.