The double affliction was the destruction of both the first and second Batei Mikdash (Holy Temples) of Jerusalem, and the double consolation in the coming Redemption through Moshiach will be the building of the third Beis Hamikdash (Holy Temple).
The consolation is “double” – even though there will only be one third Beis Hamikdash – because the third Beis Hamikdash will be eternal. The necessity for consolation over both Batei Mikdash is because each exceeded the other in a different way: the revelation of G-dliness in the first Beis Hamikdash was greater than that in the second Beis Hamikdash, whereas the second Beis Hamikdash was larger and (particularly when it was rebuilt by Herod) more magnificent than the first Beis Hamikdash, and also stood for ten years longer. The third Beis Hamikdash will combine (and infinitely exceed) the advantages of both.
