This is a personal and subjective belief, because I believe sex is a very intimate and emotional thing and that casual sex is devaluing for both parties involved (either men or women). I'd think of someone as exhibiting slutty behaviour when they demonstrate a lack of selectivity and fuck without any regard for emotional connection whatsoever.
This definition isn't that valid when people don't attribute any kind of value to sexual activity. If it's like 'cardio for two', then there are no sluts to them.
As for the double standard, it's because women are generally reluctant to have sex with a man, so sleeping with a lot of (particularly higher-quality) women is seen as a type of accomplishment. Men are generally more eager to sleep with women, so a woman who sleeps with a lot of men is seen as being easy and unselective (and therefore not worth much, because nothing worth having comes easy). Not saying it makes sense, but that's human psychology for you.
Many men will struggle with past promiscuity in women they become romantically involved with, because they can feel not 'special', or can be worried about not being able to wow her sexually, or can resent her for experiencing things they have not, or are worried about her faithfulness or they use the above logic and devalue her due to her past or get mental images of her in previous situations and rage. This gets dealt with separately:
1. You are special. She's with you, not anyone else. You're her #1 choice.
2. It sucks that she's probably had better sex with someone else than with you, but deal with it. You're with her now, you'll have time to practice.
3. Her experience pays off in being generally a better lover, and you can experience things with her. IF you find that you emotionally need more experience fucking other people or doing things she's no longer willing to do, then break up.
4. If casually dating someone, then it's a red flag, but if you've had a long, stable relationship then that's the best evidence for monogamy.
5. Relationships move one direction - forward. As long as her past stays there, move forward. If her past creeps into the present, then either deal with it or break up.
6. If dealing with mental images, they fade with time. Ask her to not discuss her past with you if it makes things harder.
There's probably some kind of ownership complex there.
On the other hand, people have to realize that past actions are rarely consequence-free. Aside from STIs, you also can deal with a social stigma and/or have the past follow you around. Good choices and a mild degree of restraint will probably keep you from getting burned.