First, you need to drop the 'the'. Sentence should read,
"I wonder if age will deepen the lines in my face when I am 40"
One of the usages of 'will' is making predictions about the future.
Here, the speaker is making a prediction (using 'will') that the lines in their face are going to deepen when they are 40.
Another example of making a prediction using 'will' is,
"She will be sick if she keeps eating too much".