The Solow model (for which the American economist Robert Solow was awarded the Nobel prize in economics in 1987) ignores the temporary ups and downs of the business cycle and explains potential income (output) as it obtains in the long run.
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The main building block is the production function. While the 3D production function shows output to depend on the capital stock and the labour force, the basic version of the Solow model keeps the labour force fixed at its normal level. We may then operate with the partial production function that keeps L fixed.
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To identify the level of (potential) income (or output) this economy generates in long-run equilibrium, we need to find out the capital stock maintained in long-run equilibrium:
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Capital is added when firms invest. Capital is lost due to depreciation. So when investment exceeds depreciation the capital stock grows; when investment falls short of depreciation the capital stock shrinks. The capital stock remains unchanged, or steady, if investment equals (offsets) depreciation. This situation is called a steady state.
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When does investment exceed depreciation, and when does it fall short of it? This can only be answered if we know what determines investment and depreciation:
As regards depreciation, we may safely assume that a constant fraction of the capital stock, say 5 percent, is lost every year because it is used up or became obsolete. Then depreciation equals 5 percent of the current capital stock. In a Y/K diagram the depreciation line (or, in a more general setting, the requirement line) is a straight line with slope 0.05.
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To determine investment, suppose there is no government and no trade with other countries. Then according to the circular flow diagram investment equals saving. Saving is a fixed share of income. Then the amount people save and invest at different capital stocks may be read off the red savings curve in the accompanying diagram.
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Whether the capital stock grows or shrinks depends on where it currently is. If it is at K₀, firms invest and buy more capital goods than they loose due to depreciation. Net investment is positive. The capital stock will be higher next year. If the capital stock is at K₁, investment fails to replace all capital that wears out. Net investment is negative. The capital stock will be lower next year.
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The crux of this is that if current capital is smaller than K*, the capital stock grows; if it exceeds K*, the capital stock falls. So the capital stock always moves towards K*, where it will stay, since only there depreciation is exactly replaced by new investment. K* is the steady-state capital stock, and Y* is steady-state income.

Further reading on pp. 228ff.
Click here for interactive applet featuring the Solow model