A steady state is a point in a dynamic model where the state variables stop changing — their time derivatives vanish: $\dot{k} = 0$, $\dot{y} = 0$. In the Solow-Swan model, steady-state capital per worker $k^*$ solves $sf(k^*) = (n + \delta)k^*$: gross investment equals break-even investment. With labour-augmenting technological progress at rate $g$, the condition becomes $sf(k^*) = (n + g + \delta)k^*$, and per-capita output grows at rate $g$ in steady state — not zero.

Think of $k^*$ as the long-run resting point the economy is pulled toward. Above $k^*$, depreciation and population growth erode capital faster than saving replenishes it, so $k$ falls. Below $k^*$, investment outpaces break-even losses and $k$ rises. The steady state is what the economy converges to, not where it is now. A higher saving rate $s$ raises the level of $k^*$ permanently but cannot raise the long-run growth rate of output per worker — that stays at $g$. This level-vs-growth result is one of the model's signatures.