Before considering any modern associations the word may have, we should look at what it meant in the centuries when classic Christians used the word.
From the Online Etymological Dictionary:
1640s, “practicing rigorous self-denial as a religious exercise,” from Latinized form of Greek asketikos “rigorously self-disciplined, laborious,” from asketes “monk, hermit,” earlier “skilled worker, one who practices an art or trade,” especially “athlete, one in training for the arena,” from askein “to exercise, train,” especially “to train for athletic competition, practice gymnastics, exercise,” perhaps originally “to fashion material, embellish or refine material.”
The Greek word was applied by the stoics to the controlling of the appetites and passions as the path to virtue and was picked up from them by the early Christians. Figurative sense of “unduly strict or austere” also is from 1640s. Related: Ascetical (1610s).
1640s, from ascetic (adj.) + -ism. Sometimes also ascetism (1830).
From the Liddell-Scott lexicon:
A. exercise, practice, training, “ἐξ ἀσκήσιος ἀγαθοὶ γίνονται” Democr.242, cf. Protag.3, Pl.Prt.323d, al.; “γυμνασίων καὶ ἀσκησίων ἐπιμελόμενοι” Hp.VM4, cf. Th.2.39; “πολεμική” X. Cyr.8.1.34; “ἱππική”IG2.478b18: in pl.,exercises, “ἔθεσικαὶ ἀσκήσεσι” Pl. R.518e, cf. Plt.294d.
II. c. gen., ἄ. τινος practice of or in a thing, Th.5.67; “ἀρετῆς” X.Mem.1.2.20; “δειλίας ἀλλ᾽ οὐκἀνδρείας” Pl.Lg. 791b.
III. generally, mode of life, profession, Luc.Vit.Auct.7; of a philosophical sect, “ἡ Κυνικὴ ἄ.” Id.Tox.27.
2. of religious sects, asceticism, Str.15.1.61,17.1.29, Ph.1.643,J.BJ2.8.10.
IV. adornment, “τῶν τριχῶν” Aeschin.Socr.18.
Asceticism is the practice of self-denial (i.e., control of one’s passions and base impulses) for the sake of the Kingdom. The practice of asceticism – called ascesis – is most often associated exclusively with monasticism, although all the faithful are exhorted to practice lesser forms of ascesis through the Church’s regimen of prayer, fasting, and repentance.
The word “ascetic” comes from the Greek root ἀσκητικός, which is turn is from the verb ἀσκέω, meaning “I train.” The Apostle Paul likens the Christian life of prayer and repentance to training for various sporting events (1 Cor. 9:24-27; 2 Tim. 4:7). As such, the methods of ascesis should not be used as ends to themselves, but as means to the end of salvation, the “prize” which the Apostle mentions in First Corinthians.
Fr George Florovsky writes:
“God has freely willed a synergistic path-of-redemption in which man must spiritually participate. God is the actor, the cause, the initiator, the one who completes all redemptive activity. But man is the one who must spiritually respond to the free gift of grace. And in this response there is an authentic place for the spirituality of…asceticism, one which has absolutely nothing to do with the “works of the law,” or with the system of merit and indulgences.”