So in the model mentioned above (the Solow growth model, which is the standard growth model), output depends on three different things. Capital, labour, and the effectiveness of labour. This last term can also be called "technology", "innovation", "Total Factor Productivity". It's represents output not due to the number of units of capital and labour.

In the Solow model the production function (how much is produced) takes the for Y=f(K,AL). That is Y (output) will be equal a function of capital, labour, and "technology/productivity".

If we think about this, we realise that output for worker is going to depend on K and A, capital and productivity. Increases in productivity (innovation) raise the level of output, as do increases in the level of capital per worker.

The issue here is, to increase the amount of capital per worker, you need more capital, and the amount of capital depends on the amount of output.

This is because we say that savings will be equal to investment (S=I) and that the amount invested/saved will be a fraction of total output, or sY. So an increase in the savings rate, s, will increase the amount of capital, which increases output. But we cannot keep increasing the savings rate, it has an upper bound. This is why in the long run economic growth per worker will be caused by increases in TFP/A/Productivity.

See this paper to look at the difference between capital accumulation and "innovation".http://www.nber.org/chapters/c10990.pdf