The word Tartarus is only found once in the Bible and that is at 2 Pet. 2:4,
"Certainly if God did not hold back from punishing the angels that sinned, but, by throwing them into Tar´ta·rus, delivered them to pits of dense darkness to be reserved for judgment;" (2 Pet. 2:4)
Notice the "pits of dense darkness". To help better understand what Tar´ta·rus is, consider the parallel text found at Jude 6:
“And the angels that did not keep their original position but forsook their own proper dwelling place he has reserved with eternal bonds under dense darkness for the judgment of the great day.”
Showing when it was that these angels "forsook their own proper dwelling place," Peter speaks of "the spirits in prison, who had once been disobedient when the patience of God was waiting in Noah’s days, while the ark was being constructed." (1 Pet. 3:19, 20) This directly links the matter to the account at Genesis 6:1-4 concerning "the sons of the true God" who abandoned their heavenly dwelling to couple with women in pre-Flood times and produced children by them, such offspring being designated as Nephilim.
From these texts it is evident that Tar´ta·rus is a condition rather than a particular location, since Peter, on the one hand, speaks of these disobedient spirits as being in “pits of dense darkness,” while Paul speaks of them as being in “heavenly places” from which they exercise a rule of darkness as wicked spirit forces. (2 Pet. 2:4; Eph. 6:10-12)
So considering the above, the "dense darkness" that the disobedient angels are in suggests a condition - not of non-existence or unconsciousness, but of - being cut off from illumination by God as renegades and outcasts from His family, with only a dark outlook as to their eternal destiny.
It is also evident that Tar´ta·rus is not the same as the Hebrew Sheol or the Greek Hades, both of which refer to the common earthly grave of mankind. This is made plain from the fact that, while the apostle Peter shows that Jesus Christ preached to these “spirits in prison,” he also shows that Jesus did so, not during the three days while buried in Hades (Sheol), but after his resurrection out of Hades. (1 Pet. 3:18-20)
For more, see:
TARTARUS - Links to Information (INDEX; Watchtower Online Library)
Tartarus (Insight-2 pp. 1068-1069; Watchtower Online Library)
“Tartarus” 2Pe 2:4—“By throwing them into Tartarus” Gr., Tar·ta·ro′sas; Lat., de·trac′tos in Tar′ta·rum; Syr., ʽa·gen ʼe·nun beThach·ta·ya·thaʼ (INDEX p. 1575; Watchtower Online Library)