In Act I, Scene 3, Laertes' words to Ophelia draw upon two meanings of the word subject.
The first is a noun, meaning "a citizen of a state." The second is an adjective, meaning "dependent upon."
When Laertes describes Hamlet as being "subject to his birth," he is saying that Hamlet is literally a subject of the king and also dependent upon family obligations. He is not simply free to love Ophelia.
Hamlet is basically the account of Hamlet and his mission for exact retribution against Claudius; nonetheless, amidst his contentions, unmistakably Hamlet has a relationship or the like with Ophelia. This relationship, in the long run, costs Ophelia her life, and it is a relationship that her sibling cautions her about, however maybe not for the right reasons. Before he comes back to class, Laertes and Ophelia have a couple of minutes together. Obviously, they cherish each other and have a transparent relationship, despite the fact that Ophelia later reproves her sibling, teasingly, about lecturing her yet not following his own recommendation about things. In this discourse, Laertes cautions Ophelia around a few particular stresses he has concerning her association with Hamlet, something she promptly confesses to having.
