If you say:

Il vit de manière simple.

It’s not expected that you give more detail about the way he is living. What is important here is "Il".

Whith:

Il vit d’une manière simple.

You mention that his way of living has something special. It’s expected that more details about this way of living will come up.

Some examples:

Il vit de manière simple car il est très pauvre.

Il vit d’une manière simple: il ne mange que de la soupe et fait ses courses à pied.