Without a common power to keep people in check, life becomes a war of all against all
Hobbes's starting premise is that human beings, considered in a hypothetical state of nature without any overarching authority, are roughly equal enough in strength and cunning that no one can feel permanently safe from anyone else. Even a strong person can be overpowered by several weaker ones acting together, or ambushed while sleeping, so equality of capability produces universal insecurity rather than stable order.
From this rough equality, Hobbes argues, flows constant competition for scarce resources, distrust of others' intentions, and a drive for reputation and glory, since being feared is one of the few reliable ways to deter aggression in a lawless environment. The result isn't necessarily nonstop violence but a pervasive readiness for it, which he calls a condition of war.
In this condition, Hobbes argues, there's no possibility of agriculture, commerce, or the arts, because no one can safely invest effort in projects that could be seized or destroyed by force. Famously, he describes life here as "solitary, poor, nasty, brutish, and short."
Takeaway: even universal capability for violence, without any authority to restrain it, is enough to make sustained cooperation impossible.