This is only a quick answer, unfortunately. The key intuitive insight for Epstein-Zin is that they separate two distinct properties of preferences: risk aversion ("I'd prefer less uncertainty to more uncertainty*") and intertemporal substitution ("I may want to shift consumption forward or backwards in time**").
In the very popular Constant Relative Risk Aversion class of preferences (CRRA), risk aversion and intertemporal elasticity of substitution are tied together as inverses of one another. Recursive preferences, and specifically Epstein-Zin, use certainty equivalence in a clever way to split out the parameter which controls intertemporal substitution from the parameter which controls risk aversion in a static gamble.
The static risk aversion parameter is embedded in the function which imposes the certainty equivalence, and the intertemporal elasticity of substitution parameter is imposed over today's certain consumption and the certainty equivalence value for utility of consumption tomorrow.
That's my attempt to describe it intuitively/verbally. It's much more precise in mathematical form -- one good exposition that I like a lot is Francios Gourio's Asset Pricing field's course notes (EC745 is the course number). You can currently find these notes, titled "Lecture Notes on Macroeconomics and Finance
Ec 745," on his website here; see section 8 on page 36.
Work through the math a few times and hopefully it will suddenly "click." The analytical idea is really quite clever. Gourio goes on to discuss how to actually estimate these models, which is very helpful.
(*The proper definitions involves preferences over "lotteries," but I think discussion of that would cloud what we care about here.)
(** by a certain percent, as a function of the interest rate.)