나라는 꿈 = 나 + -라는 + 꿈 (dream) => A dream that is me.
(It is a poetic way of referring to oneself as a being full of dreams)
X-(이)라는, short for X-(이)라고 (말)하는, makes a modifier phrase for a noun/pronoun similar to "which is called X" or "which is X", a way of adding a description (이 is added for smooth pronunciation after a consonant-ending syllable).
For example, 김영희라는 사람 (someone named 김영희), 63빌딩이라는 건물 (a building (which is) called 63빌딩), 사랑이라는 것 (what is called love).
It could also be a shortening of 나라는 꿈이다 (A country is a dream), although not very likely.