We usually talk about 'the day ahead' when we are talking about our plans for today. E.g. I've got a busy day ahead (or ahead of me) means that I've got a lot to do today.
We can also use it to descibe relative time. For example 'I need to arrive two days ahead of the conference to gove myself time to recover from the journey' (the conference starts on Wednesday, we need to arrive on Monday)