And Moshe went and told these things to all of Israel
Went where? The interpreters are divided:
- Targum Pseudo-Jonathan: He went to the study hall
- Ibn Ezra: We went to each tribal area, and perhaps announced the blessings that appear later on.
- Ramban: He went to each tent to respectfully take leave of the people
- Baal Haturim: He went to Abraham, Issac and Jacob who are mentioned in the preceding verse, and let them know the promise they received regarding the gifting of Canaan to their descendants was on the verge of being fulfilled.
- Kli Yakar: He walked the length of the camp to demonstrate that he retained the phsycial ability to lead, only God had revoked from him the authority. (and more)
Another thematically sound interpretation is provided is found in the Targum Shivim (LXX) where the words וַיֵּ֖לֶךְ מֹשֶׁ֑ה are translated as "And Moshe concluded." This marks the last paragraphs of Deuteronomy as an epilogue. The long valedictory of the previous chapters having ended, Moshe now turns his attention to concluding tasks: The charge to Joshua, the final blessings, and so on.
The Dead Sea Scrolls give a wrinkle to the LXX's interpretation. In the Sefer Devarim found at Qumran, the text reads not vayelech, but vayechal (the last two consonants are reversed) This version - which may, in fact, have been the version used by the LXX translators - connects Moshe's career with the first Creation story, and the purpose of the world (2). When the Lord finished his work the verse says וַיְכֻלּ֛וּ. Now, with his own work done, something similar is said about Moshe.
(1) In the Bible, almost all prophets make similar demurrals when God first appoints them. Make what you wish of this common motif.
(2) I expect DH aficionados will point out that Deuteronomy and the first Creation story are thought to be the work of two different hands, respectively D and P. It it true that this is the theory, but even so one mustn't rule out the possibility that the editor(s) made literary embellishments.