Back in the days of chivalry, men would kneel before lords and kings as a mark of respect, obedience and loyalty. It's also a common gesture in religious ceremonies - you kneel before God.
In the same vein, to kneel before the person you wish to marry is a sign you are pledging allegiance and respect to a person - in essence, giving yourself to someone.
If you're wondering why people began using rings, you can thank the Pope.
Pope Innocent III, in 1214, introduced a law demanding a waiting period be observed between couples wishing to marry. Couples on this period were ordered to wear a ring on their finger as a mark of their commitment.
Interestingly, the three months salary rule began as a marketing campaign in 1936 by diamond sellers DeBeers.
They successfully created a sense of luxury around diamonds, which are actually a lot less rare than you think these days.