symmetric monoidal (∞,1)-category of spectra
An $E_\infty$-ring is a commutative monoid in the stable (∞,1)-category of spectra. Sometimes this is called a commutative ring spectrum. An E-∞ algebra in spectra.
This means that an $E_\infty$-ring is an A-∞ ring that is commutative up to coherent higher homotopies. $E_\infty$-rings are the analogue in higher algebra of the commutative rings in ordinary algebra.
In terms of model categories, and $E_\infty$-rings may be modeled as ordinary commutative monoids with respect to the symmetric monoidal smash product of spectra, a fact sometimes referred to as “brave new algebra”.
Peter May with contributions by Frank Quinn, Nigel Ray and Jorgen Tornehave, $E_\infty$-Ring spaces and $E_\infty$ ring spectra (pdf)
Moritz Groth, A short course on infinity-categories, pdf.