The full text of the proposed legislation can be found here. It's easy to understand and (in this writer's opinion) very well written. Here are the key points:

The bill makes it illegal to hold in captivity a wild-caught or captive-born orca for "performance or entertainment purposes." That is defined as "any routinely scheduled public exhibition that is characterized by music or other sound effects, choreographed display or training for that display, or unprotected contact between humans and orcas. Holding of an orca is not, by itself, a performance or entertainment purpose."
The bill also makes it illegal to import or export killer whales intended for performance or entertainment. It explicitly states that this provision would be waived for transferring an orca to a sea pen or to the wild, and doesn't apply to individuals who are "held for rehabilitation after a rescue or stranding, or for research purposes."
The legislation, as written, would also end the participation of captive orcas in California in breeding programs. It would be illegal to breed or impregnate any of those orcas, and it would also be illegal to "export, collect, or import" any genetic materials from those whales "for the purpose of artificial insemination." Ostensibly this would mean that researchers could still collect genetic materials for research purposes.

California is currently home to ten orcas held in marine parks or aquaria. Three of them were captured in the wild before it was made illegal, and seven were born in captivity.

At the end of the press conference, as if on cue, a bottlenose dolphin breached the surface of Santa Monica Bay, several hundred meters behind Assemblymember Bloom. It served as a good reminder that with a little patience and luck, it's even possible to witness a performance from a wild cetacean.