In other words, you force yourself to completely ignore your crush online so that you can make an attempt to converse with them in person.
This vow prevents the insomnia and/or obsession caused by non-stop Facebook checks in order to see if the said crush has replied or paid any attention to the crush-ee.
"Yeah, she needs to take a Facebook chastity vow."
"Susan still hasn't replied to my comment! I can't stand this!"
"Dude- chill. Take a Facebook chastity vow and cool your jets"