In his sermon recorded in 2 Nephi 10, Jacob uses "isles of the sea" in a way that distinguishes the location of "isles of the sea" from the Old World whence Lehi et al. came from:
And it shall come to pass that they shall be gathered in from their long dispersion, from the isles of the sea, and from the four parts of the earth; and the nations of the Gentiles shall be great in the eyes of me, saith God, in carrying them forth to the lands of their inheritance . . . And now, my beloved brethren, seeing that our merciful God has given us so great knowledge concerning these things, let us remember him, and lay aside our sins, and not hang down our heads, for we are not cast off; nevertheless, we have been driven out of the land of our inheritance; but we have been led to a better land, for the Lord has made the sea our path, and we are upon an isle of the sea. But great are the promises of the Lord unto them who are upon the isles of the sea; wherefore as it says isles, there must needs be more than this, and they are inhabited also by our brethren. (vv. 8, 20-21)
Why is this important?
In the Book of Mormon, after the death of Jesus, there were three days of darkness (3 Nephi 8:3, 23; 10:9) while in the Old World, there were three hours (Luke 23:44). While some critics claim this is a contradiction, the fact we are dealing with different geographical areas answers such a claim (to understand the stupidity of the “argument,” it is like claiming that there being 3 inches of rain here in Tralee, Ireland contradicts someone from Atlanta in the USA who said it actually snowed that day[!]). Some critics will admit that this is not a true contradiction and instead, 1 Nephi 19:10 teaches that the entire world would experience three days of darkness:
And the God of our fathers, who were led out of Egypt, out of bondage, and also were preserved in the wilderness by him, yea, the God of Abraham, and of Isaac, and the God of Jacob, yieldeth himself, according to the words of the angel, as a man, into the hands of wicked men, to be lifted up, according to the words of Zenock, and to be crucified, according to the words of Neum, and to be buried in a sepulchre, according to the words of Zenos, which he spake concerning the three days of darkness, which should be a sign given of his death unto those who should inhabit the isles of the sea, more especially given unto those who are of the house of Israel.
However, as seen in 2 Nephi 10, there is a distinction between “isles of the sea” and the land Lehi et al came from, so “isles of the sea” in 1 Nephi 19:10 is a prophecy of the New World location where the Nephites dwelt, and it would be “especially” meaningful to those in that area who were “of the house of Israel” and would have known of the promised signs and meaning thereof (e.g., the salvific death of the Messiah in the Old World).
As for the meaning of “isle(s) of the sea,” it does not denote an island, but any area surrounded by water, such as a peninsula (like “Monster Island” for those who were fans of the Simpsons back when it was funny . . .;-) )