If you look at the Oxford dictionary, there are several meanings for blind. This is meaning 2:
Lacking perception, awareness, or judgement
So, if somebody does something blindly, they do it without thinking about it properly.
Reaching for something can mean literally extending the arm to take something, but it also has a figurative meaning of trying to attain something.
What this sentence suggests is that people sometimes buy a piano because they think that just buying the thing will somehow give them beautiful music... failing to consider that they will actually have to learn to play it.