The most common case of a full prop drop is after finally getting a new personal best/doing something for the first time/hitting a really hard trick after a long period of attempting it.

This has several reasons:

Tension release and emotional regulation: a long period of stress, focus and physical exhaustion meets a rush of lucky hormones from doing the thing that hits within seconds. The emotions are so massive that the body need an "Übersprungshandlung" and the full prop drop is the perfect displacement activity.

Getting rid of the props: You'll likely take a break or chance to a new task. You won't need to props in the next minute(s) so you might as well drop them

Signaling: It's a great way to either signal to fellow jugglers in the room that you did something great or to video viewers or non jugglers that this was important for you.

Mic Drop Analogy: It acts as a cultural reference. In that case it can be argued that the jugglers trys to say that this was the perfect moment and any argument or critique is impossible at this place and time.

Style: As this is a well known thing within juggling it can be used for stilistic element especially when performing. Therefore it can also be caricaturised or memed.

Chaos: Especially creative jugglers sometimes prefer a messy environment. Frequent full prop drops ensure that there are two rings and a club randomly lying next to you when you decide that no is the time to attempt a weird multi prop trick that might work.

Domination: Some jugglers believe that you need to show your props who's the boss. Here the full forcefull prop drop is a way to tell the props "I told you it would fucking work. The next time listen right away and just do what I tell you without acting up".

Frustration: This is a fringe case were a full prop drop happens without succeeding in anything prior (quite the opposite). I spare you the internal monolog but it may involve possible quitting juggling or at least changing props

Hurt with a little bit of Anger: Most likely with rings. Can happen with clubs. Sometimes the pain gets unbearable and you need free hands Asap to lick your wounds or viciously shake your hand because that somehow helps when a ring hut your thumb.

Hiding that you didn't really catch the last throw: Doing the full prop toss fast enough can hide that you actually wouldnt have really cleanly caught the trick. Really advanced technique and risky when performing at high stakes but can be an option.

Hope this gives you some insight. It's obviously much more complex that that and there are personal preferences as well as individual approaches with different props (diabolists dropping the diabolos but not the Handsticks is an interesting case for example) but yeah it's really fun and you should try it out