When read (as it should be) with verse 2, the "many people" is a parallel to the "nations." The emphasis is on the universality of the pull of the temple. Verse 3 makes very explicit the correlation between the mountain of the house of the Lord and the "house of the God of Jacob." The attraction to the house of the Lord, to the temple, will be that from that location God "will teach us of his ways.. for out of Zion shall go forth the law…" The temple will be the location from which the law of God will be preached.
In the last days, this will be recognized by those of pure hearts, and they will be spiritually pulled to the temple as the means of instructing them in the way to "walk in his paths."
Symbolic analysis: The last two phrases of this verse form an interested inverted paired set:
For out of Zion shall go forth the law,
And the word of the Lord from Jerusalem.
Central to the two pairs is the theme of the law/word of the Lord. Surrounding this statement are two locations, Zion and Jerusalem. In this case, they are seen as symbolically if not physically the same location. Thus the paired phrases become identical, and repeated for emphasis. It is not at all unusual for Isaiah to conflate Jerusalem and Zion, as the temple on the tops of the mountains becomes the symbolic center for the world, and Jerusalem and its temple were seen in precisely that context:
"…it follows that the true world is always in the middle, at the Center, for it is here that there is a break in the plane and hence communication among the three cosmic zones [heaven, earth, underworld]. Whatever the extent of the territory involved, the cosmos that it represents is always perfect. An entire country (e.g. Palestine) a city (Jerusalem), a sanctuary (the Temple in Jerusalem), all equally well present an imago mundi. Treating of the symbolism of the Temple, Flavius Josephus wrote that the court represented the sea (i.e. the lower regions), the Holy Place represented the earth, and the Holy of Holies heaven (Ant. Jud. III,7,7). It is clear then, that both the imago mundi and the Center are repeated in the inhabited world. Palestine, Jerusalem, and the Temple severally and concurrently represent the image of the universe and the Center of the World. This multiplicity of centers and this reiteration of the image of the world on smaller and smaller scales constitute one of the specific characteristics of traditional societies." (Eliade, 1959, p. 42-3).
For Isaiah, the sacred nature of Jerusalem places it at the center, at the location of this "temple of temples." Of course in the last days, Latter-Day Saints believe that this temple on the tops of the mountains refers to a "new Center" which flows from the Utah valley and the temple there located. While there is a physical structure in Utah, and there are physical mountains, the reference once again should be understood to be to the communicative function rather than the structure. The temple on the mountains in the last days is more truly the prophet than any building. From the context of the next verse, this establishment of the true prophetic communication might also look yet even farther forward in time.