In an economic model, we normally have a production function that increases with the amount of labour. Since inherited capital is fixed, in the short run,the only way to increase out (supply) is via increasing the amount of labour employed. The real world is somewhat fuzzier; some service industries (like software) can have greater sales without increasing the number of employees. However, such behaviour is limited, and greater output is normally associated with more people working.
The relationship between aggregate supply and aggegate demand somewhat depends on prior economic views. To summarise the Keynesian view, if aggregate demand rises (or is expected to rise), firms will increase output (hiring more labour) to meet expected increased demand.