In brief, there are three tiers of PlayStation Plus now, all offering slightly different features. PlayStation Plus Essential is the same as the 'old' service - a simple subscription with monthly free games, the ability to play online, and some extra discounts at the PS Store. Simples.
The next tier up is PlayStation Plus Extra which has all the Essential tier benefits, plus access to a catalog of up to 400 PS4 and PS5 games to play.
Then, the top tier is PlayStation Plus Premium. It has all the benefits of the previous two tiers but also adds the ability to play select PS3 games via cloud streaming, a selection of original PlayStation, PS2, and PSP titles via download or streaming, and time-limited trials for major PS5 releases.