Paul urges “supplications, prayers, intercessions, and thanksgivings.” He says these are to be made for all people. See 1 Timothy 2:1.
In 1 Timothy 2:1–2 the writer urges the community to make prayer a top priority. He lists several kinds of prayer and says they should be offered “for all people.” He then highlights rulers and other authorities as specific subjects of prayer. This call to pray comes after the letter’s opening emphasis on guarding the community from harmful teaching and promoting a life shaped by love and a clear conscience (1 Timothy 1:3–7).
The passage presents prayer as a top priority for the church’s gathered life (“first of all”). It lists several forms of praying—asking, broader praying, praying on behalf of others, and giving thanks—and places them under one broad scope: prayer is to be made for “all people” (all).
A careful answer keeps the immediate passage, the book's argument, and the whole-Bible storyline together, so the question is answered in context instead of as a detached idea.
Start with 1 Timothy 2:1, then read the surrounding section so the answer stays connected to the passage's flow.
1I exhort therefore, first of all, that petitions, prayers, intercessions, and givings of thanks, be made for all men: