Some have already answered this, but I'd like to add a bit and summarize.
1) With optical you first need to actually fire a flash. Sometimes you can fire the built-in flash. But you will contaminate the scene with that first flash. You do not want that when you really want a mood.
Radio trigger = Problem solved.
2) Optical slaves do not fire in some bright situations, not only in daylight, but also indoors where some spotlight is over one of your slaves.
Radio trigger = Problem solved.
3) Optical. You need a line of sight. This limits you on the setup.
Radio trigger = Problem solved.
4) Distances. With optical, the slave won't detect at some range. Let's say 5 m.
Radio trigger = Problem solved. Some triggers work with ranges at least 10 times larger.
You can have a flash on the other side of a room and trigger it.
5) Flash firing contamination. You are at a wedding with your optical flashes...and everyone is firing their smartphones withown flashes... you are in a trouble.
Radio trigger = Problem solved.
6) Flexibility You can fire 10 flashes across a big room if you want. That is the difference.
7) In some models you can remotely adjust the intensity of the flash from the trigger itself.
You can set up 3 groups for example, and change group A to 1/2 power, group B to 1/4, and group C to 1/8 or whatever combination you want. No need to run to your flashes.
87) And in some models you also have TTL. TTL on an offshoe flash!
Flexibility That is the difference.
Nowadays there are some cheap but sturdy radio triggers and receivers, and some flashes with radio receivers built in. Price is not a real issue anymore.