[…] Wherefore should I
Stand in the plague of custom, and permit
The curiosity of nations to deprive me
For that I am some twelve or fourteen moonshines
Lag of a brother? why 'bastard'? Wherefore 'base,'
When my dimensions are as well compact,
My mind as generous and my shape as true
As honest madam's issue? Why brand they us
With 'base,' with 'baseness,' 'bastardy,' 'base,'
Who, in the lusty stealth of nature, take
More composition and fierce quality
Than doth, within a dull, stale, tired bed
Go to th' creating a whole tribe of fops
Got 'tween asleep and wake? Well then,
Legitimate Edgar, I must have your land.
Our father's love is to the bastard Edmund
As to th' legitimate. Fine word, 'legitimate,'
Well, my legitimate, if this letter speed
And my invention thrive, Edmund the base
Shall top th' legitimate. I grow, I prosper.
Now, gods, stand up for bastards! (1.2.2-23)
In this passage, Shakespeare reveals Edmund's motives for trying to destroy his father, Gloucester, and his brother, Edgar. Edmund has been mistreated and labeled a "base" "bastard" for two reasons: 1) he's an illegitimate child, the product of Gloucester's affair with an unmarried woman; 2) Edmund is not an eldest son (Edgar was born first).
In Shakespeare's day, primogeniture (the system by which eldest sons inherit all their fathers' wealth, titles, lands, power, debt, etc.) was the rule. Edmund is not only seen as a lesser being than his older half-brother, Edgar, he also stands to inherit nothing from his father. But, Edmund objects to the way society views him as insignificant and insists that he's just as noble and well-composed as his brother, Edgar. It is here that Edmund resolves to go after Edgar's "land" as he composes a scheme for revenge.