A YL is a female Amateur Radio operator.
From the beginning a male Amateur Radio operator, regardless of age, has been called "OM" (short for Old Man). As you can imagine, polite folks didn't think it right to call a female operator "Old Woman." For that reason, the term "YL" (Young Lady) was coined.
There was a time when a married woman was called an "XYL." However, a true lady is always young at heart, and so today any female operator is called a YL. Her age and marital status have nothing to do with this proud designation.
The CW abbreviation "33" goes back many years. Clara Reger, W8KYR (and who later held W2RUF), started the practice of closing a QSO with another YL by sending 33. It was adopted officially by YLRL in 1940. It means "love sealed with friendship and mutual respect between one YL and another YL." (Thanks Nancy Rabel Hall, KC4IYD)
There was a time when YLs said goodbye by signing "88" (love and kisses). OMs also used 88 to say goodbye to a YL. Like the term XYL, 88 has for the most part fallen into disuse and that, I'm sure you'll agree, for good reasons.
Today, YLs usually sign with "73" (best regards) at the end of a QSO with an OM. However, to affirm the special bond that exists between them, YLs sign with each other by sending 33.
There are other numbered greetings you might hear on the air. For example, in recent years some folks have combined 73 + 88 to come up with "161," and it means the combination of 73 and 88. Finally, it's not used very often, but if you should hear "55," it means best success.
If this confuses you, you could do like some CBers and say, "Good numbers to you." I wouldn't do that, however.
33, Sylvia, K8SYL