For an answer that is entirely scripture-based and does not appeal to extra-biblical sources, read
HERE. In particular, read posts 14, 21, 31, and 44. In a sentence, the answer can be stated as, "
Israel is those in whom God perseveres with Christological (or salvific) purpose." It is truly that simple.
One point not mentioned in that thread is that Israel is Jesus. Matthew makes this clear when he quotes Hosea 11:1 and applies it to Jesus.
Hosea 11:1 ESV
When Israel was a child, I loved him, and out of Egypt I called my son.
Matthew 2:14-15 ESV
And he rose and took the child and his mother by night and departed to Egypt and remained there until the death of Herod. This was to fulfill what the Lord had spoken by the prophet, “Out of Egypt I called my son.”
That prophecy was about Jesus, not a geo-political nation-state. When he in whom I persevere was a child, I called my son out of Egypt. If scripture is read (all of it, from the first time the word "
Israel;" is ever mentioned all the way to its last mention with "
those in whom God perseveres" in mind a wealth of understanding is had. Very rarely does the Bible explicitly use the word "Israel" to refer to a geo-political nation-state.