This is Hamlet's third soliloquy. In his first soliloquy, in act 1, scene 2, Hamlet questions his existence, grieves his father's death, tortures himself about his mother's hasty marriage to his uncle, Claudius, and decides that "It is not, nor it cannot come to, good" (1.2.161).
In his second soliloquy, in act 1, scene 5, after he's encountered his father's ghost and been told that Claudius killed his father, Hamlet calls his mother "a most pernicious woman" and his uncle a "damned villain" and passionately vows to avenge his father's murder.
HAMLET. ... Now to my word:
It is 'Adieu, adieu! Remember me.'
I have sworn't. (1.5.115-117)
By his third soliloquy, in act 2, scene 2, Hamlet has frightened Ophelia, mocked Polonius, played at words with Rosencrantz and Guildenstern, and amused himself with the players who arrive at Elsinore.
After watching one of the players perform a passionate speech about Hecuba from a play about Aeneas and Dido, Hamlet realizes that he's done absolutely nothing to even begin to avenge his father's murder.
Hamlet scolds himself for not being able to rouse his own passion even to the level of a player acting "but in a fiction, in a dream of passion" (2.2.545), and he cries out for vengeance.
Hamlet recognizes the futility of his ranting and emotional outbursts, and he puts the logical part of his brain to work. He decides to have the players perform a play "something like the murder of [his] father" (2.2.590) so he can observe Claudius's reaction to the play and hopefully observe him acting guilty about murdering Hamlet's father, if what the ghost said is true.
For some reason, Hamlet second-guesses what the ghost said to him—something about the ghost being a devil and abusing Hamlet to damn him—and Hamlet is looking for more or better proof that what the ghost told him is true, even if that proof is likely to be wholly subjective, indirect, and circumstantial, at best.
This isn't the only time that Hamlet procrastinates about avenging his father's murder, of course, but it comes fairly soon after his previous soliloquy, in which he swore to put everything aside and focus entirely on vengeance against Claudius.