In act 1, scene 3, of Shakespeare's Hamlet, Laertes is about to embark on a ship to France (for reasons never explained in the play). His father, Polonius, advisor to King Claudius, tells him to hurry aboard the ship—"The wind sits in the shoulder of your sail, / And you are stay'd for" (1.3.60–61)—then spends the next few minutes giving Laertes fatherly advice.

The context in which the line in question appears relates to Laertes's friends, and would-be friends.

POLONIUS:
Those friends thou hast, and their adoption tried,
Grapple them to thy soul with hoops of steel;
But do not dull thy palm with entertainment
Of each new-hatch'd, unfledged comrade. (1.3.66–69)

Polonius is saying that Laertes should hold tight to his proven friends and keep them close to him but also to be wary of would-be friends until they've proven their loyalty.

Polonius uses the slightly hyperbolic metaphor "hoops of steel" to describe how Laertes should hold onto his real friends by exaggerating the bond that Laertes should feel toward them.

It's interesting to note that this is the only instance of hyperbole in Polonius's advice to Laertes. Polonius apparently feels strongly about having good and loyal friends and wants to emphasize their importance to Laertes.

Another aspect of Polonius's speech to consider is whether his advice comes from his own experience or if he's simply repeating clichés and platitudes that he's overheard, as he sometimes appears to do in other parts of the play.