It occurs when your date allows kissing even though they are not attracted to you.
This is called Baseball metaphors for sex There's normally no fifth base, and House was actually playing with the terms.
The sexual contact associated with each base has evolved dramatically since I was a teenager, although "home base" or "home run" has always meant intercourse, and "first base" has always meant kissing or snogging.
To use the expression correctly, you get or make it to a base, per my comment: quotation, if I interpret it correctly, they had intravaginal sex twice and then she performed oral sex on him.
Some people only consider French kissing as getting to first base.