Yes, it's a normal response to effective sexual stimulation... keep doing it that way for long enough and you'll have an orgasm.
An orgasm is all the things you feel and all the things that happen with your body and mind at the peak of sexual arousal and pleasure. It's a reflex we're all born with (just like knee jerks and sneezes) that our bodies have in response to sexual stimulation. You will *definitely* know when you have one. There's nothing else anywhere in human experience that feels that way.
It can take a girl or woman anywhere from a few seconds to a couple of hours to reach orgasm. Both of these are pretty unusual but perfectly normal, and anything in between is just fine... and most can get there in much less than 10 minutes when they masturbate.
Just before orgasm, you might have a feeling a bit like you have to pee, but it's not quite the same, and when your orgasm first happens, there'll be a very strong (sometimes intense and *powerful*), warm and sometimes tingly feeling that spreads from your clitoris to your vagina and then through your whole lower body. Then very quickly your clitoris, your vagina, your crotch muscles and your butt-hole will squeeze and pulse a few times while that feeling spreads all over you.
During all this, your heart will beat *very* quickly, your toes will probably curl, you might feel like you need to hold your breath or like you have to breathe really fast, your body will want to tense up and might jerk or shake or shiver, and you might make some noises (grunts, gasps, groans or cries) that you can't really control. You might "squirt" or "ejaculate" a lot of fluid from your urethra (don't worry, it's not pee).
While all of this is going on, the physical and emotional pleasure that you'll feel everywhere at the same time is just about the best feeling a human body can possibly have. Your body is producing more of its "feel good" chemicals and hormones at this time than during any other natural experience, and your nervous system's pleasure centres are cranked up to their maximum.
(Everything you "might" feel or do above isn't always going to happen... some orgasms are much less overwhelming than just *very* pleasureable.)
As that feeling becomes more gentle and starts to go away (after maybe 5 to 20 seconds), your whole body will begin to relax, your skin will flush pinker (especially over your chest) and you might feel sort of like having a nap... or like just lying there and letting your mind drift... or even like doing it again (and again... etc) right away.
It's not often, but it *can* happen sometimes that there'll be no interruption at all between several orgasms in a row, and it can feel like one single orgasm... intense physical pleasure and whole-body tension and release that can last anywhere from 30 or 40 seconds to several minutes.
Having vaginal sex alone isn't a very effective way to have orgasms for most women, because the vagina isn't the place where women's most direct sexual pleasure comes from. The clitoris is.
It might interest you to know that by the age of 12, 1/3 of all girls have already been masturbating to orgasm at least occasionally for half their lives or more... that by age 15, it's 2/3 of them doing it *regularly* (many of them more than once a day)... or that by the age of 20, more than 80% of women are doing the same - regardless of whether they've ever had intercourse.
... or that the very first thing sex therapists teach women who've never had an orgasm is how to masturbate - because that's the *only* sure fire way for a woman to learn how her body responds sexually and what will bring her to orgasm.
Masturbation is having sex with the only person you'll ever meet who knows *exactly* what you feel and what you like, even if that changes every second.
Once you can have orgasms dependably when you masturbate, you can have them dependably whenever you have sex with a partner... either by giving them to yourself during sex or by teaching your partner what works for you so *he* can give them to you.
Seriously. If you don't have orgasms alone... it's time you learned: how's your man gonna know how to get the work together with you if *you* don't even know what the job is?
One thing you can do to find out is check out the "Female Masturbation" webpage at clitical-dot-com ...
http://www.clitical.com/female-masturbation/masturbation-basics.php
http://www.clitical.com/female-masturbation/masturbation-techniques.php
(Actually, the entire section is incredibly valuable reading, but there's an awful lot of it to digest in one gulp.)
Read the pages all the way through, and try some of the things suggested. Take your time (it might take a whole afternoon the first time), and just enjoy learning what feels best for you. Sooner or later, you'll have an orgasm in one or more of these ways, and they get better each time if you're one of those lucky girls who can have them again and again.
Then you'll know what one is and how to have one, for sure.
Have fun with it and don't worry. Masturbation is normal and healthy, learning what pleases you sexually is good for you, and when it comes to having sex with the one you *want*, you'll be able to tell them (or to show them if you like) the things you like best.