symmetric monoidal (∞,1)-category of spectra
An ordinary (commutative) ring is a (commutative) monoid or algebra object internal to the symmetric monoidal category Ab of abelian groups.
The role that Ab plays among ordinary categories is played by the stable (infinity,1)-category of spectra $Sp$ among (infinity,1)-categories.
A commutative ring spectrum, or E-infinity ring, is accordingly a commutative algebra in an (infinity,1)-category.
A commutative ring spectrum is a commutative algebra object in the symmetric monoidal (infinity,1)-category of spectra.
reference to standard literature on $E_\infty$ things goes here
then..
the $(\infty,1)$-categorical perspective on commutative ring spectra is the topic of
section 7 of