On the day that the tabernacle was reared up. Here we are sent back again to the great day of Israel's sojourn at Sinai, when God took visible possession of his dwelling in the midst of them (Exodus 40:34).
Everything after that was but preparatory to the approaching departure, and therefore is narrated not in any order of time, but either as it referred back to the first day of the first month, or forward to the twentieth day of the second month.
The cloud covered the tabernacle, namely, the tent of the testimony. The testimony was the decalogue written on the two tables of stone, and enshrined within the ark, the moral law which lay at the heart of Judaism.
The tent of the testimony was the holy of holies in which the ark dwelt (see on Numbers 10:11; Numbers 18:2). The exact meaning of the words מִשְׁכָּז לְאֹהֶל הָעֵדֻח is disputed, or the rather significance of the לְ with which the phrase "tent of the testimony" is appended to the word "tabernacle" (dwelling).
Some take it as equivalent in construction to the genitive, "the dwelling of the tent of the testimony;" in which case it would simply mean that the cloud covered the whole tabernacle, the mishcan which enveloped and enclosed the ohel, which again enshrined the ark and the testimony.
Others take לְ here in the sense of "at" or "towards," and read, "covered the dwelling, towards the tent of the testimony," i.e; over that part of it in which the testimony was kept. Apart from the strict grammatical question, the comparison of other passages cited (especially Exodus 40:34) seems in favour of the first interpretation, and so apparently the Septuagint and the Targums.