Shakespeare plays upon the double meaning of the word "nature" in this scene.
The action of the scene revolves around the setting in motion of the main subplot of the play -- the hoodwinking of Gloucester by his illegitimate son, Edmund, into believing that his legitmate son, Edgar has turned against his father. Edmund is intent upon having Glocester disinherit his half-brother so that he may be the one to claim his father's lands.
The double meaning comes in at the beginning and the ends of the scene. In his opening soliloquy of the scene, Edmund confides to the audience that he is bound in "service" to the law of nature. By this, he exposes his dissatisfaction with the laws of man (rather than nature) that would brand him an outsider because he is born a bastard. He questions:
. . .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, base?
And he goes on to point out that "in the lusty stealth of nature" that he is fare more fit and suited to have position and power that the those that come from "a dull, stale, tired bed" -- meaning his brother. This argument is Edmund's reasoning for convincing his father to believe that his brother is a turncoat. In this soliloquy, Edmund examines his own "nature" as contrasted with that of his more do-gooding brother and finds his own qualities of person, not birth, to render him the superior man.
Later, once Gloucester has swallowed Edmund's story, hook-line-and-sinker, Shakepseare brings in the other meaning of "nature" when Gloucester, searching for some external cause that his true and loyal son Edgar should turn against him, blames Nature, by way of cursing the aligment of the moon and stars. He says:
These late eclipses in the sun and moon portend no good to us. Though the wisdom of Nature can reason it thus and thus, yet Nature finds itself scourged by the sequent effects: love cools, friendship falls off, brothers divide. . .in palaces, treason; and the bond cracked 'twixt son and father.
And Edmund ends this part of the scene with a scornful dismissal of this superstitious appraisal of Nature. He does not believe that the events of the stars decide his future. He believes himself to be the architect of his future not the external movements of the natural world. So Edmund believes it to be his own "nature" rather than "Nature" that decides his course.
In this scene the meaning of nature (as being one's character and tendency towards certain behaviours) is contrasted with the forces of the natural world (ie Nature). For more on "nature" in this play and Act I, scene ii, please follow the links below.