Where $p$ is a proposition
The Principle of Bivalence (PB): $p$ is only either true or false. A ball (proposition) is white(true) or black (false)
The Law of the Excluded Middle (LEM): $p \vee \neg p$. Either a proposition is true or its negation is true. Given a ball, the ball is white OR not (the ball) is white. In classical logic negation is defined truth functionally so not simply denies the stated truth value of a proposition i.e. $\neg p$ means change the truth value of $p$. In my analogy, if not meant the same then not (the ball) is white = the ball is not white i.e. the color of the ball has changed from white to not white. In a two-valued (two-colored) system, there's only one truth value/color $p$ (a ball) can be under negation, to wit, false (black).
What exactly has been excluded by LEM? The neither $p$ is true nor $\neg p$ is true. Not (That a ball is neither white nor not white): $\neg(\neg p \wedge \neg \neg p) = \neg(p \wedge \neg p) = p \vee \neg p$
Rejecting PB: An example would be to float a third truth value (color) as is done with trivalent logic.
Rejecting LEM: Amounts to paraconsistent logic and dialetheism. Contradictions can be true. A proposition $p$ (a ball) can be both true (white) AND not true (not white)