The term "blinkies" as used here means wearable circuits, usually with ostentatiously visible circuitry, which blinks lights or does something else visual (or sometimes audible). In the early days these were simple timer circuits that caused one or two LEDs to flash. These days blinkies usually use microcontrollers and can be quite impressive.
In my area of the world, specifically in midwest science fiction fandom with a hard SF leaning, they are used both as a sign of geek cred and as a teaching/learning experience, similar to (but very much predating) the current Maker Faire "learn to solder" fad. Some science fiction conventions have had workshops where anyone can come in and make their own blinkies for over 20 years.
Here's a simple 555 based blinkie. It uses a 9 volt battery to alternately blink two LEDs.
Here is the blinkie that was introduced at Duckon 20. It has ten two-color LEDs driven by an Atmel Tiny85 CPU. Microcontroller chips like this are so cheap that it really only makes sense to use 555 chips as above anymore as learning exercises.
This is a quick video shot at the prototype stage. The finished blinkie could do many different blink patterns - at this point it was just doing a simple pattern as a test.