What does this $\asymp$ symbol mean? (subject: analytic number theory)

It can mean different things depending on the context. For instance, in Graham, Knuth, and Patashnik's Concrete Mathematics it's defined to mean the same thing as "Big $\Theta$" (see p. 448), as in

$$ f \asymp g \iff \exists\, C,D>0 : C|g| \leq |f| \leq D|g|, $$

but I read a paper recently where it was instead defined to mean the same thing as $\sim$ (as defined here).

Searching further on Antonio Vargas's accepted answer above finds an insightful short paper of A.J. Hildebrand on Asymptotic Notation.

From this the following useful reference table is screenshotted below: