What does MILF mean when referring to a woman?

If you have to ask, you're too young. This word became popular after it was used in the movie "American Pie" to refer to Stifler's mother. It's an acronym for "Mom I'd Like to F..." or, translated into somewhat less vulgar, "Mother with whom I would like to have a sexual relationship." As a rule, it's used by young men: it's odd for a young lesbian to use it.

Desirable Older Woman

When someone refers to a woman as a MILF, they're saying two things: that they consider her older, at "mother" age (even if she's the same age as the mother herself), and that they find her sexually desirable. Furthermore, it refers to a woman who already has children.

It could just be a fantasy..

Perhaps the mother in question isn't open to that kind of interaction, either because she's married, isn't attracted to men, doesn't feel like relating to a young man, or simply doesn't want a relationship. The young man projects an Oedipus fantasy onto her, but since incest between mother and son is taboo in most Western societies, he diverts that desire to someone else's mother, usually the mother of another man. In the digital realm, he definitely loves perfect MILF porn vids and similar content. 

Sometimes, there are women older than the young man in question who seek out that kind of man. Men and women mature differently, and she may long for the vigor of youth, coupled with a man who desires her, or she may want a young man to spend time with out of curiosity. The reasons vary, but the desire is there.

A MILF for one man may not be a MILF for another.

While there are mothers who are desired by many young men (and some women), individual taste plays a very important role here. Some men like women of a certain height, hair color, or skin tone, from this or that social background, because she's the mother of THAT person, etc.

It's not just limited to mothers.

And not only MILFs, there are also G-MILFs! These aren't mothers, but rather grandmothers whom (perhaps not so young) men find sexually attractive. Here, it's no longer so important that they are grandmothers, but rather that they are at the age at which they are generally considered to be grandmothers.

The image of a rich, single man seeking young women to be his "sugar daddy" is familiar. The female counterpart is the "cougar" or "sugar mama." The difference between a MILF and these types of women is that the sugar mama, who may or may not be a mother, actively seeks out young men, while the MILF, in addition to being a mother, is sought out by young men. It doesn't mean "sexy old woman."

There are MILFs under thirty. The only requirements for being one are having one or more children and being sexually attractive to younger men. They can be thirty, forty, or fifty years old and still fall into this category without a problem.

It's not an expression used by an adult man.

A man the woman's age won't refer to her as a MILF unless he's still mentally under twenty-one. It's the kind of expression used by young men, minors who have recently reached puberty, teenagers, etc.

Some like to be called a MILF...

For some mothers, being called a MILF implies an acknowledgment of being desired by other men, younger than them, despite the heavy burden of having one or more children. It's like an extension of youth, an acknowledgment of possessing a certain power over young men. …and others are offended by it

For others, it's like saying, "Despite being a mother, despite being older, I'd like to have sex with you," as if reaching a certain age or having children negates a woman's sensuality. They believe that if they find them attractive, there are better ways to express it, and they see this term as offensive.