Metias's journals seem pretty benign on the surface; he's just a guy who likes to write a lot and take notes on all the activities he does on a daily basis. Nothing too out of the ordinary, right? Wrong.
In Legend, everything is about truth-seeking, and Metias's journals are another object designed to help June discover the truth. When she stumbles across a bunch of misspellings, she realizes that Metias must be leaving a message for her:
Then I hear a click, see a faint light scan across my skin, and the white page disappears. In its place appears what looks like a blog. My breath catches in my throat. There are six brief entries here. (2.10.44)
In leaving June his journals, Metias entrusts her with the real truth about the Republic—even though it happens to be particularly ugly. It's a call for her to do the right thing because he knows that she's a good person and that she won't let these injustices slide—and for June, it's also a way for her to still connect with her brother even from beyond the grave.
Metias may be dead, but the Iparises are still united in their quest to bring justice to the citizens of the Republic. The journals make it so that Metias's presence is there even in June's most confused and desperate moments.