Redactive analysis: This verse is an interesting transition paragraph, allowing Nephi to mix his time frames and media. He has moved from a written lecture for a future audience to a historical description of his oral teachings to his people, and uses that orality to introduce not only the historical reference, but the current textual inclusion. The Isaiah passages that follow were read to his people, and Nephi writes them in this text as part of the record he desires to leave.
The Isaiah texts immediately following are included for a specific message - the stated redemption of Israel in Jerusalem also applies to the Nephites who are also separated, and awaiting a redemptive restoration to their ancestral House.
Nephi's Self-Perception: "The Isles of the Sea":The phrase "isles of the sea" is not absolutely unique to Nephi, but is used in Nephi in such as way to make it an important concept for Nephi's self-understanding. Of the ten occurrences of the phrase in the scriptures, eight of them are in Nephi's writings. To understand Nephi's usage, it is important examine the way the phrase is used in the other two examples:
Esth. 10:1 And the king Ahasuerus laid a tribute upon the land, and upon the isles of the sea.
The usage in Esther is obviously to known lands as it entails a tribute. While "isles of the sea" could be either specific or generic (as a term for "everywhere") it is certainly referencing the known world.
The usage in Isaiah may be the more generic usage of the term:
Isa. 24:15 Wherefore glorify ye the LORD in the fires, even the name of the LORD God of Israel in the isles of the sea.
Here it is not clear whether or not there are specific locations indicated. It is most likely that "isles of the sea" is a euphemism for "everywhere" in this passage.
This usage is directly contrasted to Nephi, however, where Nephi considers himself to be on one of the "isles of the sea":
2 Ne. 10:21 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.
In this verse Nephi is citing promises to those on the isles of the sea, and specifically notes that because it is in the plural, that it must indicate "more than this." Nephi clearly believes that they are on one of the isles of the sea, and uses this verse to speak of their scattered brethren on other islands of the sea.
Nephi's understanding of their location certainly stems from two sources. The first, and most obvious, was that they crossed an ocean to arrive at their location. That Nephi would not have know that they were on a continent rather than an island is certainly not surprising given the geographical knowledge of the times, and the little time that Nephi and his people would have had for exploring. A more important reason, however, is that Nephi had a theological reason for associating his people with the isles of the sea.
In his readings of the brass plates Nephi obviously reads Zenos, and finds in Zenos a reference to a gathering from the isles of the sea:
1 Ne. 19:16 Yea, then will he remember the isles of the sea; yea, and all the people who are of the house of Israel, will I gather in, saith the Lord, according to the words of the prophet Zenos, from the four quarters of the earth.
When combined with Nephi's clear perception of his people on the isles of the sea, the connection between Nephi's concerns for his lost Jerusalem (for example 1 Nephi 19:20) and his desire for a gathering of his people as well as all of Israel becomes obvious. When likening the scriptures to their own needs, the gathering from the isles of the sea strikes a very strong emotional chord in Nephi who so poignantly remembers the separation from Israel.
While Nephi clearly makes this connection, it is a connection and a description that fades from the Book of Mormon, and is never used after Nephi ceases to write.