"고" is a verb/adjective conjugation ending indicating a connection between two events like English "and". it expresses a simple sequence or enumeration of events without any deeper relationship between the two. 밥 먹고 갈래요 literally means "I will eat and go" (먹다 + -고, 가다 + ㄹ래요(I will; I intend to)), which is a sequence. The sentence can also be said as question too, which will then be "Would you like to eat before you leave?". Another example of a sequence: 일을 모두 마치고 퇴근했다 (I finished all the work and left for home). An example of an enumeration: 인생엔 기쁜 일도 있고 슬픈 일도 있다 (There are both joyful and sad things in life). There is one special use of -고 in "-고 싶다" form, which is a set expression for "like to" or "want to". Ex) 먹고 싶다 (I like to eat). 가고 싶다 (I want to go). 그만두고 싶다 (I want to quit).