The wall suggests a clear demarcation between those who are in and those who are out. Scholars note that the revelation is extremely low on imperatives and yet despite this a strongly moralistic view of the world undergirds it: there will be those within the heavenly city, and those outside of it.
What does it mean to say that the wall was jasper? In Rev 4:3, we find that the person on the throne is "like a jasper." So what does the person on the throne and the wall have in common? Perhaps we are seeing a symbolic representation of Jesus' "I am with you alway[s], even unto the end of the world" (Mt 28:20, which is even more interesting in Greek where the "with you" interrupts the "I am" in a striking example of form following function.)
When the holy city descends in 21:11, the light is described as being like a jasper stone. So the one on the throne, the light emanating from the city, and the wall of the city--not to mention one of the foundations of the city (see v19, where jasper gets pride of place as the first foundation)--are all associated with the jasper stone. The point seems to be to suggest a unity between these elements. Unpacking that a little, I would conclude that the city itself is meant to be identified with the one on the throne and that whatever light it has comes from him.
pure and clear
The same Greek word, katharos, is used to describe the gold and the glass, even though the KJV chose to translate it once as "pure" and once as "clear." While the semantic range of katharos covers both pure and clear (as well as clean), it strikes me as suspect to translate the same word two different ways in the same sentence. One could have translated it as:
The city was clear gold, like clear glass.
The city was pure gold, like pure glass.
And yet both of those would raise their own questions. For the first option, what would it mean to say that gold is clear? For the second, what would it mean to say that the pure gold was like pure glass? (Does this not also imply that it is clear?) Why has the gold lost its opaqueness and become transparent (a word that some translations use here)? If the entire city is transparent, what does that say about life in the city? What might this symbolize?
19 And the foundations of the wall of the city were garnished with all manner of precious stones. The first foundation was jasper; the second, sapphire; the third, a chalcedony; the fourth, an emerald; 20 The fifth, sardonyx; the sixth, sardius; the seventh, chrysolite; the eighth, beryl; the ninth, a topaz; the tenth, a chrysoprasus; the eleventh, a jacinth; the twelfth, an amethyst.
Note that the gems appear to correspond generally to the gems in the high priest's breastplate. (See Exodus 28:17-20; John's list omits four from Exodus and adds four others from the LXX; the order is also different, but the four that have been swapped out appear to be "semantic equivalents" NIGTC, page 1080). The point seems to be that the very foundations of the city are (or: are decorated with) the breastplate of the high priest. What were the functions of the high priest's breastplate? In what ways would the foundation of the new Jerusalem serve those same purposes? It is very difficult, in an LDS context, to avoid the conclusion that in a general sense, the foundation stones of the city are symbols of priesthood authority/power. Exodus 39:8-14 suggests that the breastplate formed a pouch containing the Urim and Thummim, which then would suggest that the entire city here is the (a?) Urim and Thummim. What would that symbolize for the city's residents?