The literal meaning of the Arabic and Quranic term ‘Fasiq’ is one who intentionally and constantly transgresses the clearly prescribed boundaries of Allah (Subhana wa tala). The basic verb derived from the referred root means "he disobeyed". From a purely literal perspective, the subject or the nominative form of this verb (i.e. Fasiq) would mean "the one who disobeys". So it comes from the root word, "Fa-Seen-Qaaf which is a verb in Arabic and its doer is noun ie, Fasiq.
Fasiqun is an Arabic term referring to someone who violates Islamic law. However, it is usually reserved to describe someone guilty of openly and flagrantly violating Islamic law and/or someone whose moral character is corrupt.
And We have certainly revealed to you aayaath [which are] clear proofs, and no one would deny them except the defiantly disobedient(Fasiqun). Quran Surah Baqarah 2:99
The word “Fasiq” appears approximately 37 times in the Quran always condoning with a negative connotation as a fasiq declines to the commands of Allah. It applies to one who has taken upon himself to observe what the law ordains and has acknowledged it’s authority and then has fallen short of its observance in respect of all or some of its ordinances. Even though the word can be interchangeably used with the word munafiq and kaffir, the meanings vary. The word fasiq has more general application than the word kaffir because even a Muslim can in his heart be a FASIQ. Allah said: Who break the covenant of Allah after contracting it and sever that which Allah has ordered to be joined and cause corruption on earth. It is those who are the losers. Quran Surah Baqarah 2:27 
Narrated by `Abdullah, The Prophet, said, "Abusing a Muslim is Fusuq (evil doing) and killing him is Kufr (disbelief). Sahih al-Bukhari Vol.1:48 and Vol.9:7076 (OE Vol.9: 197) 
Shaikh Salih al Fawzaan said,
Fisq, linguistically, coming forth from, and in the Sharee'ah(it means) departing from the obedience of Allah. It comprises the total departure from obeying Allah which is applicable to the infidel, and it comprises partial departure of obedience which is imputed to a believer who commits a major sin.
Fisq is of two categories,
a. Which constitutes apostasy, i.e. infidelity; in that case a Kafir is called Fasiq, as Allah called Iblees saying: "And disobeyed (Fasaqa) the command of his Rabb." Quran Surah al-Kahf 18: 50
This type of Fisq on the part of Iblees constituted infidelity. And Allah says: "And for those who are disobedient (Fasaqu), their abode will be the Fire." Quran Surah as-Sajdah 32: 20
Allah meant the infidels by 'disobedient' as indicated by His (next) Words: "Whenever they want to come out of it (the Fire) they will be turned back into it, and it will be said to them, 'Taste the punishment of the Fire which you used to deny." Quran Surah as-Sajda 32: 20
b. Although disobedient Muslim is called 'Fasiq', but his Fisq does not cast him out of the folds of Islam, such as those to whom Allah refers in the following verse: "And those who calumniate chaste women and do not bring four witnesses, flog them with eighty lashes, and never accept their testification thereafter, and it is they that are the Fasiq." Quran Surah an-Noor 24: 4
Allah also says: "So whoever decides to perform the pilgrimage in these months, should remember that there is no foul talk, not any Fusuq nor argument during the Hajj season." Quran Surah al-Baqarah 2: 197