"Thanks for that. There the grown serpent lies. The worm that's fled hath nature that in time will venom breed." What is the context and significance of these lines from Macbeth?
Macbeth has hired murderers to kill Banquo and Fleance, his son, while the pair travels on the road, because he fears that Banquo's descendants will eventually take his throne from him. He says that the Weird Sisters
[...] hailed [Banquo] father to a line of kings.
Upon my head they placed a fruitless crown
And put a barren scepter in my grip,
Thence to be wrenched with an unlineal hand,
No son of mine succeeding. If 't be so,
For Banquo's issue have I filed my mind;
For them the gracious Duncan have I murdered [...]
To make them kings, the seeds of Banquo kings. (3.1.65-75)
Macbeth is angry and bitter because he killed his kinsman and friend, the former king Duncan, so that he could ascend to the throne, and now someone else's kids are going to benefit from it. In order to thwart this prophecy, Macbeth plans to have Banquo and his son killed.
When the murderers come to the banquet to report to Macbeth, they are forced to tell him that they were only able to kill Banquo, and that Fleance escaped. Macbeth uses a metaphor to compare Banquo to a "grown serpent," and he feels safe that Banquo will pose no further threat to him because he cannot sire more children. However, Macbeth continues the metaphor to compare young Fleance to a "worm," a baby snake that doesn't have venom to injure Macbeth yet, but will in time. Fleance could become king, or his son could. Shortly after Macbeth receives this news, Banquo's ghost actually comes to the banquet to frighten him, and because Macbeth has not informed his wife of his intention to have Banquo murdered, she thinks Macbeth is hallucinating, seeing the ghost of Duncan.
Remember that the weird sisters, in Act I, told Macbeth and Banquo their fates. Macbeth would be thane of Cawdor and king, but would not sire kings. Banquo would never be king but would sire a line of kings. Once he is crowned, Macbeth become increasingly paranoid, and one of the first things he does is hire murderers to kill Banquo and his son Fleance. The leader of the cutthroats has just come to Banquo's castle to report that Banquo is "safe"--meaning "safe in a ditch," dead--but Fleance escaped.
Macbeth responds: "Thanks for that. There the grown serpent lies." That is, Banquo, the "grown serpent," is dead. He goes on to say: "The worm that’s fled / Hath nature that in time will venom breed; No teeth for th' present." He's here referring to Fleance, who is not yet old enough to breed, as a "worm" (a baby snake in this instance). He says he still is a threat because, in time, he'll have venom (when he's older), but he's no threat right now.
Macbeth has failed to change Banquo's fate, and his son will begin a line of kings, the most recent of which--at the time the play was performed--was understood to be King James I, the new king of England, Scotland, and Ireland. This is the king Shakespeare wrote the play for, so Macbeth is the bad guy and Banquo and his progeny are the good guys.