It means, generally, “maiden”, and can conceivably mean “young woman of marriageable age” (although there is no clear example in the Bible of it meaning this, it was given this meaning in later rabbinical literature, possibly as a redefinition specifically to contradict the Christian understanding), but is forced by context to mean “virgin”, as the context is that of asking for a miraculous sign “as high as heaven or as deep as the pit”, and a young woman of marriageable age giving birth is not miraculous in the least, nor is it a sign for Isaiah to have predicted what he would be named (Immanuel, “God with us”), as some Jews claim the intended miracle or sign is supposed to be.
See, when the Jews translated the Septuagint, of which LXX Isaiah is from probably 100 years before Christ, it was translated by Jews and for Jews: and at that time, the LXX translators translated “almah” to the Greek “parthenos”, which unequivocally means “virgin”, having the same semantic range as the English word “virgin” (e.g. “parthenos” can never be used of a sexually-experienced woman or girl): at the time, before Christ, the Jews, at least in Alexandria (which was the center of Jewish scholarship), believed that “almah” meant “virgin”; a later redefinition blurred this to “maiden” or “young woman”, and modern redefinition even further redefined it to exclude the original understanding of “virgin” altogether: but, when Isaiah was written, and when the Septuagint was translated, both centuries before Christ, the original audience and translators both understood the word to mean “virgin”. Contrary evidence, even amongst other Jewish writings, is virtually non-existent until Christians began using said passage to as a proof-text against Judaism, leading (understandably) to a desire to change the definition of the word that they were being beaten over the head with in to a softer shape (to mix metaphors).
Think of the development of the English word “prevent”: in the King James Bible, it means generally “to come before”, with the implication of a coming-before to prepare the way for what follows, so that either Rome or the man of sin could be spoken of as “prevent the coming of antichrist”. Today, in the same context, “prevent” has the diametrically-opposite meaning. Instead of the man of sin “preventing” (coming before and preparing the way for) antichrist, we would understand it as the man of sin “preventing” (blocking the appearance of) antichrist - and this is the development of language with no especial guidance behind it, as one may posit at least a basic guidance (in Jews wishing to make the Scriptures less able to support the Christian claim) in the redefinition of “almah”. Once “prevent” meant to prepare; now it means to oppose. “Almah”, in Biblical times and at least through the times of the LXX translation, was understood to mean “virgin”: only later, with this being used as a prophecy and proof of Christ and Christianity, did it come to be redefined, at first to mean “maiden”, and then “young woman” generally.
But this meaning is foreign to the Bible, even if it is at home in the later rabbinical writings and especially mediaeval texts, and became ever-more-prominent on the Christian side to the point of going mainstream with the publication of the RSV, rooted in modern anti-supernaturalist liberal religion and higher criticism in the 19th century. It became more prominent on the Jewish side with the growing acceptance of Jews and the decline of anti-Semitism (so that Jews could propagate their new understanding of the word): understand that (sadly) through most of Christian history, a Jew would have been liable to penalties up to and including death, and possibly inciting a wave of anti-Semitic violence, if he were to publish a book (assuming he could even arrange for a printer, which was rare until the “Enlightenment”) amongst Christians attacking Christian orthodoxy in any way. Even in the Enlightenment, when the heretical Jew Spinoza attacked Christianity (and Judaism, for that matter), he didn’t attack it as a Jew: he attacked it as an “Enlightened” philosopher (i.e. atheist, which was just as bad then, and still got him exiled, etc.).
The word which liberals and Jews say should have been used in Isaiah if God had wanted to communicate the idea that it was a virgin who would give birth is “bethulah”, and, unlike “almah”, there are clear examples in the Bible of the word “bethulah” being used of women who have had sexual intercourse, thus proving that it could not possibly have “virgin” as a primary meaning. In the Bible, there are no clear-cut examples of “almah” being used of non-virgins, so, on the balance of evidence, it appears that God used the right word in inspiring Isaiah to prophesy, just as he is always found to do on closer inspection.
