The phrase "impossible dream" refers to a goal or desire that is extremely difficult or unlikely to achieve. It represents a dream or aspiration that may seem impossible, but the person still strives towards it with determination and hope.
Tell a child he can't dream impossible dreams for himself, go ahead, I dare you.... (religion.blogs.cnn.com)
Strong enough to make even impossible dreams come true. (mymommymanual.com)
Through a rigorous academic program, relentless support, and parenting education, we are all about making the seemingly impossible dream come true. (blog.publiccharters.org)