In act I, scene 2, Hamlet speaks at length of the “the trappings and the suits of woe" and of “all forms, moods, shapes of grief, / That can denote me truly” to emphasize the difference between seeming and being—between appearance and authenticity.

In her advice that he cease grieving, Gertrude refers to her son’s “knighted colour,” or black mourning clothes. Hamlet builds on this, referring to “my inky cloak” and “customary suits of solemn black” to emphasize that such conventions are just that: customary. When he speaks of sighing and crying (“windy suspiration of forced breath, . . . the fruitful river in the eye”), in referencing the eye, he responds as well to her request that he support his country: “let thine eye look like a friend on Denmark.” Outward looks, Hamlet emphasizes (in four lines that begin with “Nor” or “No”), cannot be genuine. In contrast, his interior state is one of genuine grief: “I have that within which passeth show.”

At the end of this scene, after Gertrude and Claudius exeunt, Hamlet delivers his soliloquy on the solidness of flesh, ending with the line that contains “break, break my heart,” confirming that he is truly suffering.

Seems, madam! nay it is; I know not 'seems.'
'Tis not alone my inky cloak, good mother,
Nor customary suits of solemn black,
Nor windy suspiration of forced breath,
No, nor the fruitful river in the eye,
Nor the dejected 'havior of the visage,
Together with all forms, moods, shapes of grief,
That can denote me truly: these indeed seem,
For they are actions that a man might play:
But I have that within which passeth show;
These but the trappings and the suits of woe.

*All quotes are taken from the Norton Shakespeare, based on the Oxford Edition.

In Act I, Scene 2, Queen Gertrude and King Claudius have announced their marriage; then they attempt to convince Hamlet to stop grieving over the death of his father.
Queen Gertrude explains that death is a part of life, to which Hamlet agrees; however, Queen Gertrude still does not understand why Hamlet is taking the death so personally if he knows that death is a part of life ("...Why seems it so particular with thee?").
Hamlet explains that it does not "seem" to be personal--it is personal. It is not just the black he wears or his desperate sighs, he is truly grieving ("These indeed 'seem',/For they are actions that a man might play...").