The particle -밖에 is very similar to -만 and some might even say they are synonyms of each other. However, this is not the case both particles are different in a meaningful way and thus you ought to keep them in mind as different particles.
As mentioned, on a first glance -밖에 seemingly is a synonym to the particle -만. They both indicate that everything is excluded save for the noun it is attached to. With them, you say there is simply no possibility for anything else. However, they are not the same because there is still a very meaningful difference. The emotions behind the particle. The emotion -밖에 evokes is particularly negative and the number involved is very (too) small. It informs others you are disappointed or sad over it all. The particle -만 does not carry this emotion.
가: 왜 사과가 없어요? 장을 보러 안 갔어요?
나: 장을 보러 시장에 갔지만 배밖에 안 남았어요.
A: Why are there no apples? Didn’t you go grocery shopping?
B: I went to the market to shop, but there were only pears left.
How To Use
Using the particle -밖에, like the particle -만, is not difficult whatsoever. To attach it to a noun you needn’t worry over consonants or vowels as you simply need to attach it to the noun. After that, there is one particular rule to -밖에 you need to keep in mind. All sentences that utilize the particle need to be negative. This means instead of using 있다, you use 없다; instead of 이다, you use 아니다; and for other verbs, you use negative forms like -지 않다 or -지 못하다. Furthermore, propositive and imperative forms cannot be used with this particle.
Lastly, do make sure not to confuse the particle 밖에 and the preposition -밖 (outside) with the particle -에, which forms also 밖에. Sentences with the preposition may or may not be negative, whereas with the former they need to be written with negative forms.