The slope of the production function is the marginal product of capital $MPK$. It represents how much extra output a worker produces when given an extra unit of capital:

We can examine how $MPK$ changes with $k$:

As each worker gets its hands on more capital, the production function becomes flatter, indicating a diminishing marginal product of capital. This is because with a small amount of capital, an extra unit of capital for the average worker is very useful and produces a lot of additional output. With a lot of capital, workers given additional units of capital can only increase output slightly.

We now examine the effect of $\alpha$ on the production function:

For a small $\alpha$, aggregate output depends mostly on the number of workers. Hence marginal increases in capital do not lead to large increases in output both in aggregate and at the per-worker level. In the extreme case of $\alpha = 0$, output is independant of the amount of capital.

For a large $\alpha$, aggregate output depends mostly on the amount of capital. Hence marginal increases in capital lead to large increases in output both in aggregate and at the per-worker level. In the extreme case of $\alpha = 1$, output is a linear function of the amount of capital.