adventuresinkorean:

This is a contrastive ending with multiple usages. Some of its usages overlap with ~지만, or ~거나/~든지.

In the first use, ~(으)나 is applied exactly like ~지만 to express a contrast between two different states of affairs. Both forms are used in both writing and speaking, but more often in formal writing.

값은 좀 비싸나 음식 맛은 좋아요. 
It’s a bit expensive, but it tastes good.

어제 술집에 갔으나 술은 마시지 않았어요. 
I went to a bar yesterday, but I didn’t drink any alcohol.

의견에 따르긴 하겠으나 결과는 책임지지 않겠습니다. 
I’ll follow your decision, but not take responsibility for the result. 

좋은 약은 입에 쓰나 몸에 이롭다. 
Good medicine is bitter to the mouth but good for the body.

In the second use, ~(으)나 is used twice in the same sentence to give the meaning of “whether… or…”. Its usage implies that the state of affairs given in the final clause will occur regardless of the two choices given in the first clause. Its function here is similar to ~거나 or ~든지. 

그 사람은 자나 깨나 술만 마셔요. 
Whether awake or asleep, he always drinks.

앉으나 서나 허리가 앞아요. 
Whether sitting or standing, my back hurts.

좋으나 싫으나 해야 해요. 
You have to do it whether you like it or not. 

In the third usage, ~(으)나 can be used in clauses containing question words like ‘무엇’, ‘어디’, ‘누구’, ‘언제’, and ‘어떻게’ to imply that whatever is expressed in this clause is of no consequence. These constructions usually translate as “whoever”, “whenever, “wherever”, etc.

내가 어디 가나 상관하지 마. 
Wherever I go, just mind your own business.

뭘 먹으나 살이 안 쪄요. 
Whatever I eat, I don’t gain weight. 

In the fourth usage, ~(으)나 can be used to link two identical adjectives, in order to give emphasis to the adjective in a similar way as adding “very”/“really” or using a superlative.

크나 큰 죄인이 되고 말았어요. 
S/he ended up becoming a really big criminal.

작으나 작은 피해도 없게 하는 것이 행정의 원칙이다. 
The principle of administration is to avoid even the smallest damages.

In the fifth usage, it is combined with the verb 말다 (to desist) in the form ~(으)나 마나 to give the meaning of “whether… or not…”, and shows that the final result will occur whether or not the first clause happens. Sometimes, ~(으)나마나 is simply followed by ~이다 in the form ~(으)나마나예요.  

학생들은 혼내주나 마나 마찬가지예요. 
It’s all the same whether or not you give students a hard time.

시험은 보나 마나 그 학생은 떨어질 거예요. 
The student will probably fail whether he takes the exam or not.

그런 회의는 하나 마나 예요. 
It won’t do any good whether or not we hold that kind of conference.

(Info and examples taken from Korean: A Comprehensive Grammar and Using Korean: Guide to Contemporary Use)