Actually, there are as many definitions of courstship as there are people using it. That is one of the problems. The way I use it is 'to be in a relationship with the clear goal of marriage from both partners'.
What does that mean? You skip the dating fase. While everyone else is having dates with a romantic overtone, stick with going out with friends, doing things in groups, go to the movies do whatever... but keep out the romance, just get to know as many people you like and learn to cultivate friendships. If you can't hold on good friendships, you're not ready for marriage anyway. Because the irritations that you get in long friendships are the same irriations you'll have to learn to live with in a marriage.
Then, when you feel ready to get married, look around to see if there are people that you think might become a good partner. Only then allow your heart to open for romance. A lot of people say 'you can't chose who you love'. That's true and that's not true. You can't chose who you fall for. So even during the fase where you arent looking for romance, you might have those episodes where you feel all jittery and butterfly like. The trick then is to keep yourself under control and not to feed into those feelings. Keep befriending the person. Who knows, when you're ready for marriage, he might be the one. But don't fall into the trap of immediately starting down the path of romance and giving away part of your romantic heart when you're not ready to part with it, and he's not ready to cherrish it.
When you are ready for marriage, open your heart to romance and find a person for whom it beats faster, but... have a few guidelines here as well. If you have a good relationship with your family, it's important that your family aproves of your choice. They know you and they're not blinded by romance, so... they have a clearer view of this person and how he would fit (or not) with the whole of your person. Only allow yourself to become romantically involved with someone who is also seeking to marry. Otherwise you might be in a courtship while he might just be 'dating' you. When you know eachother well enough, when you know that you have both the romance, but also the qualities to build a steady life together, that your views mesh with eachother (this doesn't mean agreeing on everything) then you can go further towards engagment and marriage. That to me, is a courtship.
Other definitions include: allowing your parents or extended family search for a husband for you (though you ultimately keep the final yes or no of course!), chaste dating, etc.