Let's start with what it's not like, so that nobody will be disappointed. It does not have the stark grandeur of the Alpujarras, the Sierra de Cazorla, or the Sierra de Grazalema. In height, it is about equal to England's highest mountains, but it has two things that they do not have and nor do those mentioned above.
First, it is forested right to the top in most places and deciduous trees play a major part in this. Secondly, there are castles, churches, or mosques on most of the peaks, which are not forested.
There are enough way-marked walks to fill a number of holidays. If you are fit and like walking, this would be the best way to see it. Otherwise, a car would be very useful, as the bus service is limited and there is only one useful train line with only two trains a day each way.
The wildlife is said to be extensive, though I only saw a fairly scant amount. However, this included an imperial eagle [rare] flying over the hilltop at Cortegana.