Laertes advises Ophelia that Hamlet, as a Prince, has to think of the state and not in his own heart when it comes to choosing a mate. They are worried that Hamlet and Ophelia will have a relationship outside of marriage, and then Hamlet will be forced to marry someone else for the good of state. At that point, Ophelia's 'honor' will be taken and she will be unlikely to find a husband.
Within the context of the times, the advice is reasonable. Royalty often married for political reasons and not for love, and Ophelia may indeed have been left without a husband, something which would have been very hard in those times.
Act I, scene 3 begins with Laertes bidding Ophelia farewell as he is leaving for France. Laertes offers advice to Ophelia regarding Hamlet. Although Hamlet has professed his love for Ophelia, Laertes reminds his sister that Hamlet is a prince and is forced to marry due to his obligations to the kingdom:
"Perhaps he loves you now,/And now no soil nor cautel doth besmirch/The virtue of his will; but you must fear,/His greatness weighed, his will is not his own,/For he himself is subject to his birth." (Lines 14-18)
Ophelia's father, Polonius, offers similar advice. The two men are concerned for Ophelia, and they don't want to see her get hurt or marry someone who does not truly love her. He warns her to protect herself because she is young and inexperienced in the matters of the heart: "...think yourself a baby/That you have ta'en his tenders for true pay,/Which are not sterling [genuine]. Tender [protect] yourself more dearly,/Or--not to crack the wind of the poor phrase,/Running it thus--you'll tender me a fool." (Lines 105-109)