Do both sentences have the same meaing?
It's an indescribable feeling. and It's impossible to describe a feeling.

Question

Do both sentences have the same meaing?
It's an indescribable feeling.  and  It's impossible to describe a feeling.

Answer

Agree with Nancy on this. The first phrase "it's an indescribable feeling" talks about a specific feeling in a given situation. While "it's impossible to describe a feeling" talks about general feelings being hard to describe. If you made the second phrase "It's impossible to describe THIS feeling" then the phrases mean almost the exact same thing.

Answer

Not quite. Change the 2nd sentence to "It's impossible to describe THIS feeling"; then they will match up.