means to never quit or never let go in search of what you seek in your life ..... I think it is =).

The translations above are correct, but the English sounds odd to me. Perhaps it's British or Australian, or from a poem or an old novel. In the USA, it would be more natural to say "Don't cast your dreams away", or even better (for American English) is "Don't throw your dreams away".

I didn't hear this expression before =s... but CAST OFF means to get rid of something. So, yeah... could be something like : Don't forget about your dreams OR don't leave your dreams behind. =)

set aside, leave, forget or throw away..

cast off means " to discard or reject". So this sentence means "don't dicard your dream."