First of all consider what he means by 'Faith'. He's making an argument about what the law teaches, so in that context consider:Depending on your favorite translation, Hebrews 11:1 reads:
"Now faith is the substance of things hoped for, the evidence of things not seen."
Some religious folks believe that their faith itself is evidence that what they have faith in is actually true. This is particularly the case, it seems, when it comes to supernatural claims or ones that don't have good evidence for them.
In my view, this is a manifestly absurd and circular position. People believe all kinds of things, some true, some untrue. The fact that I believe, for example, that the world is flat, is not evidence that I'm correct about that.
Do you believe faith is the evidence of things not seen? Why or why not?
Look at Hebrews 10 as a preface to Hebrews 11. It begins with "The law is only a shadow of the good things that are coming—not the realities themselves." In chapter 11 he proceeds through making his argument commenting in 10:22 "...let us draw near to God with a sincere heart and with the full assurance that faith brings..." He is building a case that the law is rather than an end point a teacher of something. He implies in 10:23-26 that we have to consistently work hard at love and doing good deeds and that the opposite is to continue sinning. In other words its a sin to not be doing something good. This goes beyond what the law says. This is the furtherance and the lesson he's saying that law teaches. Hebrews 10:36 says "You need to persevere so that when you have done the will of God you will receive what he has promised."
To make a sensible answer consider what he means by 'Faith'. A supporting question is whether he thinks belief equals faith, and its clear that he doesn't. Now his statement makes more sense, and we can see that it is faithfulness that is evidence of things not seen.