I have read somewhere that after the 1000 year reign of Moshiach, there will be a destruction of this Olam Hazeh (pls. help me out, there's a word for it starting with a chet), before we go to Olam Habah. Does this destruction mean the annihilation of the material world (b/c we will no longer have need for physical bodies in the world to come)?
From the Talmud (Sanhedrin 97A):
In Torah Ohr 51D, the Baal HaTanya quotes the Sefer HaTemunah (not sure who that is), saying that the world exists in a series of 7000 year cycles (analogous to the Shmita cycle) [This is based on the Talmud quoted above], and we are presently in the second cycle. The world exists for 7000 years, is destroyed, and the next cycle starts.
The first cycle was a cycle of Kindness (the first of the 7 Kabbalistic emotional attributes), while the cycle we are in now is the cycle of Severity (the 2nd of the 7 Kabbalistic emotional attributes).
Other Kabbalists who followed the Sefer HaTemunah explain this to mean that we will have a total of seven 7000 year cycles, one for each of the 7 emotional attributes.
The Baal HaTanya then brings the AriZal's view. The Arizal holds (see there for sources) that only in the second cycle (our cycle) is there an actual, physical world. The first cycle was only spiritual. [I think the Arizal disagrees with the other Kabbalists who say there will be 5 more cycles]
The cycle that preceded the one we're presently in refers to the spiritual world of Chaos (Olam HaTohu) and our cycle is the world of Tikkun (Order)
See here for an explanation of the worlds of Tohu and Tikkun.
See here as well:
and in footnote 298:
There is an argument between the Ramban and the Rambam over what is the ultimate reward.
According to the Rambam, the order will be:
According to the Ramban, however, the order is different:
One proof supporting the Ramban's opinion that resurrection is higher then Gan Eden is from the fact that all Tzaddikim (righteous people) like Moses will be resurrected (and will not just stay in Gan Eden).
All this, however, will all take place in the sixth millenium.
Regarding the seventh millenium, the Gemara says (Sanhedrin 97a) that "Six thousand years the world will exist and for one it will be destroyed".
There is an argument as to what does this "destruction" refer.
In this world will be the ultimate reward for our current service of Hashem, and in it will be the completeness of our current service. In other words, in that time all our current service (to bring G-dliness into this world) will be revealed in a physical way, so that there will be (in a way) a destruction of the world - in Hebrew, "world" comes from the same root as concealment. In this time period, there will be no more concealment of Hashem.