A formal/literary adjective meaning difficult or hard to do/accept/understand; often appears attached to verb stems to form expressions meaning 'hard to ~'.
信じ難い話だが、事実として記録されている。
It is a hard-to-believe story, but it is recorded as fact.
彼の提案は理解し難い点が多かった。
There were many points in his proposal that were difficult to understand.
この状況を受け入れ難いが、対処しなければならない。
It's hard to accept this situation, but we must deal with it.