The speech you mention is when Brutus is rationalizing to himself the reasons for committing the assassination of Caesar. He is revealing that he fears the power that Caesar could potentially have. He is afraid that, with power, Caesar may become a tyrant. He uses the metaphor of a serpent to suggest this, saying that a serpent may be innocent as an egg, but it will grow up and be dangerous, as Caesar might. So it should be killed as that egg, not when it can get strength:
And therefore think him as a serpent's egg
Which hatch'd would as his kind grow mischievous, And kill him in the shell.
What is interesting is that Brutus admits that Caesar has not behaved badly, or as a tyrant:
to speak truth of Caesar,
I have not known when his affections sway'd
More than his reason.
But Brutus is so scared of the power being abused, and of his country suffering, that he is willing to kill his friend to prevent it, as this speech demonstrates.