In the
Lidell-Scott Greek-English Lexicon we see that one of the meanings is "family":
"genea,, a/j, Ion. geneh,, h/j( h`, Ep. dat. geneh/fi: (gi,gnomai): I. of the persons in a family, 1. race, stock, family, Hom., etc.; Pria,mou g. Il.; evk geneh/j according to his family, Ib.; geneh/| by birth-right, Od.; geneh.n Aivtwlo,j by descent, Il.:-of horses, a breed, Ib.:-generally, geneh,n in kind, Hdt.:-also a tribe, nation, Persw/n g. Aesch. 2. a race, generation, oi[hper fu,llwn geneh. toih,de kai. avndrw/n Il.; du,o geneai. avnqrw,pwn Ib. 3. offspring, Orac. ap. Hdt.; and of a single person, Soph. II. of time or place in reference to birth: 1. a birth-place, geneh. evpi. li,mnh| Gugai,h| Il.; of an eagle's eyrie, Od. 2. age, time of life, esp. in phrases geneh/| new,tatoj( presbu,tatoj youngest, eldest, in age, or by birth, Hom. 3. time of birth, evk geneh/j Hdt.; avpo. g. Xen."
The correct translation of the following passage is as follows:
"So likewise ye, when ye shall see all these things, know that it is near, even at the doors. Verily I say unto you, This family shall not pass, till all these things be fulfilled" (Mt.24:33-34).
The family refers to the physical descendants of Abraham, Isaac and Jacob.
The Lord Jesus' sermon foretold of the "great tribulation," a time when Israel will be attacked unmercifully in an attempt to destroy the whole family of Abraham, Isaac and Jacob. Therefore it would not be unusual for the Lord Jesus to assure them that they will not be wiped out and that they will continue to exist. Therefore, He told them that the family of Abraham, Isaac and Jacob would still be in existence when He returned to the earth.
In fact, this is not the first time that such assurance had been given to the Israelites, as witnessed by these words:
"Thus says the LORD, Who gives the sun for light by day And the fixed order of the moon and the stars for light by night, Who stirs up the sea so that its waves roar; The LORD of hosts is His name: If this fixed order departs From before Me, declares the LORD, Then the offspring of Israel also will cease from being a nation before Me forever" (Jer.31:35-36).
According to the Lord as long as the sun and moon remain in the sky the nation of Israel will remain "being a nation" before Him. So there is nothing odd about the Lord Jesus telling the Israelites that "this family shall not pass till all these things be fulfilled," especially with the great tribulation in view.