Why does marginal cost slope upwards after the minimum point?
The variable unit in the quotation is the factor of production that is varied keeping the others fixed. For example it could be the amount of workers hired, while keeping the amount of machinery (capital) fixed. Or it could be the amount of machines reented, keeping the amount of workers fixed.

As for your other question diminishing returns does not refer to workers specifically, although it can. 

Suppose we do consider workers as variable input and keep capital fixed. In the beginning usually adding workers will increase output a lot, so the costs of producing an additional unit are low, and might even be decreasing. 

However, at some point adding extra workers will increase output only a little. After all the amount of capital is fixed so adding extra workers mean that they e.g. have to wait for another at the machines or get in another's way. So at that point whereas earlier you only needed say 1/2 a worker to produce an additional unit of output, now you need 2 extra workers to produce that one extra unit. That means that the costs of producing an additional unit (the marginal costs) have risen.