The Bible itself gives the meaning in this case. Consider these other references to virginity:
The virgin the daughter of Zion hath despised thee, and laughed thee to scorn; the daughter of Jerusalem hath shaken her head at thee, 2 Kings 19:21. Again I will build thee, and thou shalt be built, O virgin of Israel, Jeremiah 31:4. Set thee up waymarkers, make thee high heaps: set thine heart toward the highway, even the way which thou went: turn again, O virgin of Israel, turn again to these thy cities, Jeremiah 31:21. Clearly, these are allegorical, spiritual references. Here is an explanation on Revelation 14:4:
"Virginity is not meant to be taken literally in this place. If it
were, the five foolish virgins, Matthew 25:1-13, would be included on
the ground of their virginity, not excluded on the basis of their
folly. Besides, even in the spiritual sense here intended, the
integration of each characteristic with every other is implied, in
order to bring forth the sevenfold perfection indicated. No one
feature can be singled out as in itself a sufficient characteristic.
Then, not virginity literally. Were that so, it would exclude the
worthies so highly commended for their faith in Hebrews chapter 11.
For they were married. They begat children. Then they were not virgins
literally. But they must have been virgins spiritually, else they
would not have been set forth by the Holy Ghost as those whose example
we should follow. That is, men such as Abel, Enoch, Noah, Abraham,
Sarah, Isaac, Jacob, Moses, Gideon, Samson, Jephthae, David, and the
prophets. And will any dare exclude these? But they were not virgins
literally.
Then they must have been virgins spiritually. They must have cleansed
themselves from all filthiness of the flesh and spirit, perfecting
holiness in the fear of God. This must have been their virginity... of
purity and chasteness in being wholly separated to God and to his
things...
Indeed, if literal virginity were intended, it would be essential to
salvation. [But] 'Concerning virgins I have no commandment', 1
Corinthians 7:25?... Again he sayeth, 'And if a virgin marry, she hath
not sinned.' And to conclude the matter, hear the Hebrew epistle:
'Marriage is honourable in all' - mark that: all - 'and the bed
undefiled' - notice: undefiled - 'but whoremongers and adulterers
God will judge', Hebrews 13:4.
Then the passage 'for they are virgins', like the former introductory
clause, must be spiritual, after this manner: 'For I am jealous over
you with godly jealousy: for I have espoused you to one husband, that
I may present you as a chaste virgin to Christ.' 2 Corinthians 11:2.
Here the apostle refers to the entire - it is you, plural -
ecclesia or church, gathered at Corinth. But I speak concerning
Christ and the church." The Revelation of Jesus Christ, John
Metcalfe, pp. 356-8
http://www.johnmetcalfepublishingtrust.co.uk/contact_us.htm
Now the query about what it means for those symbolic 144,000 people not being defiled with women. Consider...
"The form of the defilement is not specified, but, from plain new
testament exhortatory passages, one would naturally suppose such
defilement to be limited to fornication, adultery, uncleanness, and
suchlike fleshly lusts. But this is not a plain new testament
exhortatory passage, it is the mystical Book of the Revelation, with a
text couched in symbolism, allegory, and imagery...
The meaning to the spiritual Israelite, or to the prophets or seer in
the old testament, went further and deeper than fornication, adultery,
or uncleanness... being 'defiled with women' had a far more specific
meaning than the general condemnation of fleshly lusts. It was
precise. It focussed particularly upon what became a snare to Israel
again and again." (Ibid. pp. 350-1)
Then follows many examples of how the people of Israel kept being lured into idolatry by the surrounding pagan nations. They formed marriage alliances that God had forbidden. Even some of the kings of Israel led the nation into spiritual defilement, setting a bad example themselves by allowing pagan wives to set up idolatrous worship, right inside Israel. See 1 Kings 114-8 & Ezra 9:1-14.
"With Ezra, or with the old testament saints, it was a question of
defiling that which was holy... This was a matter for the men of
Israel, to keep the charge. They were not to defile that which was
holy with women from the nations about them. They were not to mingle
the holy seed with the heathen. It was not that women were defiled
with men. The men had the charge, and were not to defile
themselves... (Ibid. p. 354, bold emphasis mine)
In the new testament generally the spiritual answer to this appears in such passages as 1 Corinthians 6:18,19 & 3:16,17 & 6:15 & 2 Corinthians 6:14-7:1. Please study those passages to get the spiritual meaning that applies in Revelation.
"In Revelation, fornication, defilement, must be seen as spiritual.
Regarding women, [this] passage seems to have application:
'Notwithstanding I have a few things against thee, because thou
sufferest that woman Jezebel, which calleth herself a prophetess, to
teach and to seduce my servants to commit fornication, and to eat
things sacrificed to idols,' Revelation 2:20. Now to suffer this, to
sit under or submit to the teaching of women as such and particularly
those in the character described as 'Jezebel', with their abandon and
wanton licence in defiance of all fear of God and true worship, this
is to be defiled with women." (Ibid. p. 356)
As for your third query, "what caused the need for them to be redeemed? Was it some other form of defilement or sin?" - all sinners need to be redeemed from all sin. All who will be redeemed to stand before the throne of God in heaven, whether of the 144,000 class, or the "great crowd that no man could number", have to be redeemed from their sin first.
