There were several Tarquins. The reference to his "ravishing strides" suggests an allusion to Tarquin the Proud (Lucius Tarquinius Superbus). He was a tyranical ruler who was eventually overthrown (some say as a fallout from the rape of Lucretia, others for his arrogant and evil rule). Lucretia, like Duncan, was known for her virtue. Tarquin was attracted to her but because she was virtuous, the only way he could have her was through a violent rape that eventually cost her her life (she committed suicide). The story parallels in some way Macbeth's attack on virtue (Duncan) and establishes for the audience a suggestion that if Macbeth were to claim the throne he would reign as Tarquin did--with arrogance and tyrrany.
In this monologue, Macbeth is preparing to murder the king. Essentially, he is so worried about the act he is about to commit that his mind is playing tricks on him. First, he is unable to grasp the dagger, then he thinks he sees blood on the dagger; however, he comes to the conclusion that these manifestations are a result of his nervousness.
Prince Tarquin is known for raping the Roman matron, Lucrece; therefore, this allusion is very appropriate as it seems Macbeth is attempting to evoke the prince's tyrannical spirit in order to proceed with the murder.
Let's not forget that Tulia, Tarquin's wife, manipulated her husband so that he would kill the king to gain power and wealth- Which is exactly Lady Macbeth's role in the play.
In this monologue, Macbeth was already attempting to murder the King Duncan, under the influence and manipulation of his devious wife. He had a guilty conscience about the horrible act that he was doing, which will lead to grave consequences and he knows that one wrong act would destroy his future or even his life so his mind was jumbled up with confusing thoughts and unexplained answers, playing with his brain and forcing it to submission. He became so hysterical that he fel that there was blood on the dagger, which there wasn't, which causes illusions to form in his brains and madness to ravaged his mind to a point of complete madness, but all these are only tricks playing against his pitiless brain.
The notorious Roman Prince Tarquain was known menacingly for his tyrannacy and his totalitarian control over the whole empire, but was later successfully overthrown. He had also rape Lucrece, wife of Collatine. He was trying to create an imagery that he can behave madly and cruelly like Tarquain himself and he can unleash his inner demons and sprits to reign terror and fright over the whole earth.