$A\vee \
eg A$ is a tautology in classical (i.e., Aristotelian) logic because you can prove that using the deduction rules of the classical proposition calculus no matter what the truth value of $A$ is, the truth value of $A\vee \
eg A$ is always true. That is the meaning of tautology.
In non-classical logical systems, such as intuitionism or constructivism, $A \vee \
eg A$ is not a tautology. There the interpretation of $P \vee Q$ is not "either P or Q is true" but rather the more constructive "Either I have a proof of P or I have a proof of Q". A famous example to illustrate this is the following: Theorem: There exist two irrational numbers $a,b$ such that $a^b$ is rational. A classical proof can go like this: if $\sqrt2 ^\sqrt2$ is rational we are done. Else, consider $(\sqrt2^{\sqrt2})^{\sqrt2}=\sqrt2^2=2$, a rational. Classically this finishes the proof but constructively it is not a valid proof since it does not actually show which one of the two candidates works.