if an escort says she provides a girlfriend experience, what is that exactly?

The best answer is that you should expect an experience that involves the appearance of a boyfriend/girlfriend experience, i.e., she should show some empathy and interest, not just lie back and wait for you to finish.

There should be some kissing and making out and pleasant conversation.

In reality, most of the time, it's just marketing hype and since nearly every provider states that they are GFE, the reality is that it varies greatly.

Go by the reviews for a better way to determine whether or not you'll be happy with a particular provider.

GFE and it's ilk (PSE, HME) are loosely defined terms to describe service packaging and the overall thrust of your experience with them.  It should be emphasized that the definition is LOOSE and NOT well defined across the hobby.  Your best bet is to look at the specific services discussed in reviews and make your determination from those, not from the broad description.  

In general though I've found those accurately advertising GFE tend to be more about setting up a comfortable environment, they include some degree of kissing and they may NOT go for the services included in PSE (e.g., anal, toys, bdsm-ish, etc).  

I've never quite figured out what the HME's (HoneyMoon Experience) differentiators are, unless it includes the woman being tired, drunk and having you take off her bridal gown.  Doesn't do much for me.

GFE to me means that first I'll invite you in and tell you I'm almost ready. Then I'll disappear in a cloud of perfume to the bathroom because I just need to finish my make-up. Thirty minutes later I'll come up for air long enough to parade 5 outfits past you, asking you with each one if it makes me look fat, if these shoes would look better than those, and if you think this outfit shows off my legs.

Then we'll take a 15 minute time out so that I can yell at you for your monosyllable responses to my questions.

After an hour or so we'll finally get into your car where I will give you the silent treatment all the way to the restaurant. At the restaurant, I'll order the most expensive item on the menu, asking that nearly every single ingredient be substituted in the entree for lower fat or calorie alternatives. When my dish arrives, I'll nibble on two bites before exclaiming that I'm full and couldn't eat another bite. In the meantime, while we await our culinary delights, I'll tell you my entire life history, including every single ex bf I've ever dated, complete with a list of every single shortcoming or fault they had. When I've run out of ex bf's to tell you about, I'll start telling you about my over protective mother, and my crazy uncle. At least once or twice I will interrupt you while you are chewing on your leg to get away and ask you what you are doing.

Once the dinner ordeal is over, we'll head back for my place where I will grudgingly invite you in for coffee (since you seem like a nice boy). I'll offer you coffee and sit all the way at the other end of the couch with a stop watch in my hands waiting for you to finish your cup. For atmosphere, I'll put on the soundtrack to Jerry McGuire, and positively GUSH over the scene where Tom Cruise says "You........compLETE......ME" and look at you with bright eyes waiting for you to agree that this line WAS in fact the most romantic line EVER. When you don't I'll get a little misty eyed, and slide further away on the couch.

At some point you'll decide you might as well at least get a kiss for all of your misery, and you'll circle in for a landing. I will promptly smack your face and look at as if you just described in detail how you intend to molest every female in my family, and inform you that I am NOT that kind of girl.

Finally throwing in the towel, you leave with a bright red palm print on your face, blue balls, and head for the nearest burger joint to get a real meal.

So there you have it. That is what you can expect.

NOTE: I"m kidding!!!!

I loved that - took me back to the good old days!