First, it is supposed to convince Moscow to refrain from what the United States sees as aggressive actions and to make it clear that Washington will retaliate.
The second point is engagement with the Russian side on issues of strategic interest to the United States, including Syria and North Korea, as well as cybersecurity. In particular, Tillerson wants to seek coordination with Russia in fighting the Islamic State terror group, which is banned in both countries, more actively. As for North Korea, it is supposed to reverse the growth of trade between Russia and North Korea in order to isolate Pyongyang.
The media also noted that, unlike Obama's times, the State Department became the main author of the Russian strategy, whereas in the Obama administration the National Security Council of the White House was responsible for this.