Hamlet hesitates to kill Claudius because he wants to be certain that Claudius is guilty.
Hamlet reenacts a murderous scene, searching for a visible sign of guilt from Claudius.
Hamlet cautiously searches for a definitive, visible sign of guilt. He wants to be absolutely certain of Claudius' guilt.
This is a tragic flaw for Hamlet. His insistence upon finding visible guilt from Claudius delays his action of killing Claudius, thus delaying the avenging of his father's death.
Hamlet's procrastination is well reasoned in that he desires to know the truth in reference to his father's murderer.
Nonetheless, Hamlet's procrastination allows Claudius time to suspect Hamlet's actions of avenging his father's death.
Claudius has Hamlet banished in a plot to have Hamlet killed.
Although Hamlet's hesitation to kill Claudius is an honorable quality, it is a tragic flaw that costs Hamlet his life, ultimately.
One part of an answer is in the first scene of the play during the changing of the guard: "For this relief much thanks; 't is bitter cold, / And I am sick at heart." In Act 3, scene 3, while it is not as cold indoors, it is late at night and Hamlet must be tired. Another is found in ROMEO AND JULIET: "God shield I should disturb devotion"(ROM4.1). Hamlet still has only the speech of the Ghost as evidence, it seems. Then there is the question of morality and other things.