Although modern usage has rendered this term virtually meaningless to most people, it's original meaning and usage clearly indicate "moral purity" upon the basis of "sexual purity." Contemporary usage implies "repression" or "abstinence," which have nothing to do with real chastity. True chastity is a rejection of impure sexuality. True chastity is pure sexuality, or the activity of sex in harmony with our true nature, as explained in the secret doctrine. Properly used, the word chastity refers to sexual fidelity or honor.
The generative energy, which, when we are loose, dissipates and makes us unclean, when we are continent invigorates and inspires us. Chastity is the flowering of man; and what are called Genius, Heroism, Holiness, and the like, are but various fruits which succeed it. - Henry David Thoreau, Walden
On me may chastity, heaven's fairest gift, look with a favouring
eye; never may Cypris, goddess dread, fasten on me a temper to dispute,
or restless jealousy, smiting my soul with mad desire for unlawful
love, but may she hallow peaceful married life and shrewdly decide
whom each of us shall wed. - Medea by Euripides
Be sober, diligent, and chaste; avoid all wrath. In public or in secret ne’er permit thou any evil; and above all else respect thyself. - Pythagoras
The man who by chastity preserves himself pure, fears no judgment for he is united with the name of the Holy One. - The Zohar
In the Christian church of the middle ages, gloves were always worn by bishops or priests when in the performance of ecclesiastical functions. They were made of linen, and were white; and Durandus, a celebrated ritualist, says that "by the white gloves were denoted chastity and purity, because the hands were thus kept clean and free from all impurity." - The Symbolism of Freemasonry by Albert G. Mackey 
Even St. Thomas Aquinas, the well-known Catholic philosopher, clearly stated that chasity is sexual purity:
We must next consider chastity: (1) The virtue itself of chastity: (2) virginity, which is a part of chastity: (3) lust, which is the contrary vice. - Summa Theologica
Early Church Fathers considered chasity as having three grades:
In regards to chastity as related to purity, St. Thomas Aquinas argued in his Summa Theologica:
"Augustine says (De Perseverantia xx): "We must give praise to purity, that he who has ears to hear, may put to none but a lawful use the organs intended for procreation." Now the use of these organs is the proper matter of chastity. Therefore purity belongs properly to chastity.
I answer that, As stated above (OBJ), "pudicitia" [purity] takes its name from "pudor," which signifies shame. Hence purity must needs be properly about the things of which man is most ashamed. Now men are most ashamed of venereal acts, as Augustine remarks (De Civ. Dei xiv, 18), so much so that even the conjugal act, which is adorned by the honesty [*Cf. Q] of marriage, is not devoid of shame: and this because the movement of the organs of generation is not subject to the command of reason, as are the movements of the other external members. Now man is ashamed not only of this sexual union but also of all the signs thereof, as the Philosopher observes (Rhet. ii, 6). Consequently purity regards venereal matters properly, and especially the signs thereof, such as impure looks, kisses, and touches. And since the latter are more wont to be observed, purity regards rather these external signs, while chastity regards rather sexual union. Therefore purity is directed to chastity, not as a virtue distinct therefrom, but as expressing a circumstance of chastity. Nevertheless the one is sometimes used to designate the other."
In regards to chastity as distinct from abstinence, St. Thomas Aquinas argued in his Summa Theologica that "chastity, which is about venereal pleasures, is a distinct virtue from abstinence, which is about pleasures of the palate."
"Brahmacharya or spotless chastity is the best of all penances; a celibate of such spotless chastity is not a human being, but a god indeed... To the celibate who conserves the semen with great efforts, what is there unattainable in this world ? By the power of the composure of the semen, one will become just like Myself." - Sri Sankaracharya
In Hinduism, chastity is known as Brahmacharya (Sanskrit).
Brahmacharya is a divine word. It is the sum and substance of Yoga. Brahmacharya is the Achara or conduct by which you attain or reach Brahman (God). It is life in the Absolute. It is movement towards God or the Atman (Self).
Brahmacharya is absolute freedom from sexual thoughts and desires. It is the vow of celibacy. It is control of all the senses in thought, word and deed.
Brahmacharya is not mere bachelorhood. There should be strict abstinence not merely from sexual intercourse but also from auto-erotic manifestations, from masturbation, from homosexual acts and from all perverse sexual practices. It must further involve a permanent abstention from indulgence in erotic imagination and voluptuous reverie.
In a narrow sense, Brahmacharya is celibacy. In a broad sense, it is absolute control of all the senses. The door of Nirvana (liberation) or perfection is complete Brahmacharya.
celibacy is to a Yogi what electricity is to an electric bulb. Without celibacy no spiritual progress is possible. It is a potent weapon and shield to wage war against the internal evil forces of lust, anger and greed. It serves as a gateway for the bliss beyond, and opens the door of liberation. It contributes perennial joy and uninterrupted bliss. It is the only key to open the Sushumna (the chief among astral tubes in the human body running inside the spinal column) and awaken the Kundalini (the primordial cosmic energy located in the individual).
There cannot be any language without words. You cannot draw a picture without a canvas or a wall. You cannot write anything without paper. Even so, you cannot have health and spiritual life without celibacy.
An established celibate will not feel any difference in touching the opposite sex, a piece of paper, a block of wood, or a piece of stone. A true celibate only can cultivate Bhakti (devotion). A true celibate only can practice Yoga. A true celibate only can acquire jnana (wisdom).Brahmacharya is meant both for men and women. - Sri Swami Sivananda, Brahmacharya (celibacy)
There are four processes in the practice of celibacy. First control the sex-impulse and sex-Vasana (sex-desire). Then practice conservation of sex-energy. Shut out all holes through which energy leaks. Then divert the conserved energy into proper spiritual channels through Japa, Kirtan, selfless service, Pranayama (practice of breath-control), study, vigilance, self-analysis, introspection and Vichara. Then have conversion or sublimation of the sex-energy. Let it be converted into Ojas (spiritual energy) or Brahma-tejas (spiritual halo) through constant meditation or Brahma-Chintana (remembrance of God).According to Yogic science, semen exists in a subtle form throughout the whole body. It is found in a subtle state in all the cells of the body. It is withdrawn and elaborated into a gross form in the sexual organ under the influence of the sexual will and sexual excitement. An Oordhvareta Yogi (one who has stored up the seminal energy in the brain after sublimating the same into spiritual energy) not only converts the semen into Ojas, but checks through his Yogic power, through purity in thought, word and deed, the very formation of semen by the secretory cells or testes or seeds. This is a great secret. - Sri Swami Sivananda, Brahmacharya (celibacy)