This quote is from Lord Montague, Romeo's father, in the first scene of the play. The play begins, of course, with a brawl in the street between members of the Capulets and Montagues. Romeo's mother, Lady Montague, after expressing relief that he was not involved, asks Benvolio if he has seen her son. Benvolio responds that he has seen Romeo skulking about the nearby woods, clearly distracted and upset about something. Montague replies that Romeo has been like this for some time, returning home at dawn only to lock himself in his room, and utters the quote referenced in the question. Basically, this means that he is worried about Romeo's mood, and hopes that someone can, by giving him good counsel, get to the root of his unhappiness and thus help him make it go away.

Romeo arrives on stage at this point, and in conversation with Benvolio, reveals that it is being "out of her favour/where I am in love" that is causing his fit of melancholy. It emerges that he is in love with Rosaline (though he does not say her name in this scene,) who has not only refused his advances, but has apparently decided to live a life of celibacy, which devastates Romeo:

For beauty, starv'd with her severity, 
Cuts beauty off from all posterity.
She is too fair, too wise, wisely too fair, 
To merit bliss by making me despair. 
She hath forsworn to love, and in that vow
Do I live dead that live to tell it now.

After having asked Benevolio if he has seen their son, a concerned Lord Montague speaks of Romeo's despressed behavior,

Away from light steals home my heavy son
And private in his chamber pens himself,
Shuts up his windows, locks fair daylight out
And makes himself an artificial night.
Black and portentous must this humour prove
Unless good counsel may the cause remove. (1.1.133-138)

In these lines of Lord Montague, there is the introduction of the light/dark motif and foreshadowing of the future importance of night for Romeo and Juliet. Romeo's father feels that Romeo's behavior bodes badily for him as it is not healthy to shut oneself away; he urges Benevolio to bring Romeo out of his dark mood.  Clearly, there is an ominousness about this passage, and the readers/audience may feel that tragic events are to follow as well. In addition, these lines of Lord Montague are indicative of the emotional nature of Romeo, who runs from the daylight and hides himself away to brood over the loss of the love of Rosaline.