When Jesus said "aionios" He meant, eternal, everlasting, unending,etc.
“αιωνιος/aionios” occurs 72x in the N.T.
“aionios” is translated world only 5 times in the N.T. [2%]
“aionios” is correctly translated “eternal” 42 times in the N.T.[52%]
“aionios” is correctly translated “everlasting” 25 times in the N.T.[34.7%]
Jesus used “aionios” twenty eight [28] times, [38.8% of total] Jesus never used “aionios” to refer to something common, ordinary, mundane etc. which was not/could not be “eternal.”
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…..Some people claim that “αιων/aion//αιωνιος/aionios never means eternity/eternal” because a few times they refer to things which are not eternal e.g. “world.”
However, neither word is ever defined/described, by adjectives or descriptive phrases, as meaning a period of time less than eternal, as in the following NT verses.
…..Jesus used “αἰώνιος/aionios” twenty eight [28] times. Jesus never used “aionios” to refer to anything common, ordinary or mundane that was not/could not be eternal.
…..In the following ten verses Jesus defines/describes “aionios” as “eternal.” Lk 1:33, John 6:58, 10:28, 3:15, 3:16, 5:29, 3:36, 4:14, 6:27, 8:51
[1] Luke 1:33
(33) And he shall reign [basileusei Vb.] over the house of Jacob for ever; [αιωνας/aionas] and of his kingdom [basileias, Nn.] there shall be no end.[telos]
In this verse the reign/basileusei, the verb form of the word, is "aionas" and of the kingdom/basileias, the noun form of the same word, "there shall be no end.” “Aionas” by definition here means eternal, no end.
[2] John 6:58
(58) This is the bread that came down from heaven. Your ancestors ate manna and died, but whoever feeds on this bread will live forever.[aionios]
In this verse Jesus juxtaposes “live aionios” with “death.” If “live aionios” is only a finite age, a finite period is not opposite “death.” Thus “aionios” by definition here means “eternal.”
[3] John 10:28
(28) I give them eternal [aionios] life, and they shall never [aion] perish; no one will snatch them out of my hand.
In this verse Jesus parallels “aionios” and “aion” with “[not] snatch them out of my hand”, and “never perish.” If “aion/aionios” means “age(s), a finite age,” that is not the opposite of “[not] snatch them out of my hand’/never perish” “Aionios life” by definition here means “eternal life.”
[4]John 3:15
(15) That whosoever believeth in him should not perish, but have eternal [aionion] life.
[5] John 3:16
(16) For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting [aionion] life.
In these two verses Jesus parallels “aionion” with “should not perish,” twice. Believers could eventually perish in a finite age, by definition “aionion life” here means eternal or everlasting life.
[6]John 5:24
(24) Verily, verily, [Amen, Amen] I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting [aionios] life, and shall not come into condemnation; but is passed from death unto life.
In this verse Jesus parallels “aionios” with “shall not come into condemnation” and “passed from death unto life.” “Aionios” does not mean “a finite age,” by definition here it means “eternal,” unless Jesus lets His followers come into condemnation and pass into death.
[7]John 3:36 He that believeth on the Son hath everlasting [aionios] life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him.
In this verse Jesus juxtaposed aionios life with “shall not see life.” If aionios means an indefinite age that is not opposite “shall not see life” By definition aionios means eternal.
[8]John 4:14 But whosoever drinketh of the water that I shall give him shall never [ου μη/ou mé] thirst; but the water that I shall give him shall be in him a well of water springing up into everlasting [aionios] life.
In this verse Jesus paralleled aionios with “shall [ου μη/ou mé][fn] never thirst.” If aionios means an indefinite age that is not opposite “shall never thirst.” By definition aionios means eternal. See footnote [fn] on “ou mé” below.
[9]John 6:27
(27) Labour not for the meat which perisheth, but for that meat which endureth unto everlasting [aionios] life, which the Son of man shall give unto you: for him hath God the Father sealed.
In this verse Jesus contrasted “aionios meat” with “meat that perishes.” If aionios means an indefinite age that is not opposite “meat that perishes.” By definition aionios means eternal.
[10]John 8:51
(51) Very truly [amen amen] I tell you, whoever obeys my word will never [ou mé eis ton aiona][fn] see death."
In this verse Jesus juxtaposes “unto aion” with “never see death.” By definition “aion” means eternity.