When Lady Capulet asks Juliet how she feels about marriage, Juliet's reply is to say, "It is an honour I dream not of" (I.iii.70). One thing she means in saying this is that she simply does not feel ready for marriage. At the age of 13, while it was common in this time period to be married at that age, she is still very young and probably still wants to enjoy being young and having as much freedom as would be allotted to a girl her age in that time period. If she were married, she would become her husband's property, and that is not an "honour" she presently desires for herself.
Another thing she could mean by saying she does not want the honor of marriage is that she knows she is likely to be forced into an arranged marriage, which was customary for girls of her class in that time period. Naturally, an arranged marriage can be a very frightening prospect for a girl to think about, particularly a girl Juliet's age.
Finally, another thing Juliet can mean by saying that she is not interested in marriage is that, as such a young girl, she actually may not really feel an interest in boys yet and, therefore, is not inclined to marry yet. Hence, as the play progresses, we see Juliet mature from a young girl into a woman when we see her so very suddenly transition from not wanting to marry to being desperate to marry Romeo.