성장하다 means "equip oneself in all one’s finery" (훌륭하고 화려하게 잘 차려입다.) 차려입다 means "dress up" 성장하다 in the meaning of dressing is an old-fashioned word and is rarely used nowadays.

It didn't give me an example sentence. :(

No, they are not the same at all. Your dictionary says like that? Go figure. Why don't you tell me the example sentence from your dictionary? and we'll see what it really means.

Ok. So 성장하다 in no way means the same as 차려입다? My dictionary said that 성장하다 could mean "to dress up."

차려입다 means to dress up. You could say 우리엄마는 친척의 결혼식에 가려고 한복을 차려입었다. or 그는 저녁만찬을 위해서 차려입었다.