I've heard a lot about ND filters, but what's the purpose behind them? Are they worth the money?   

For most flyers, there's no need for them.
If you have Hollywood aspirations, try them when you know more about them.
A good general rule is .. if you have to ask if you need them, you don't.

Which high quality filters are recommended for the Mini 3 Pro ?

Because the Mini series drones have a fixed aperture, this limits the control you have over exposure.
In general photography/videography you will have three veriables for exposure, Shutter Speed, Aperture and ISO.
But on the Minis you only have Shutter Speed and ISO that can be altered.
You ususally want to keep the ISO on the lowest setting to reduce grain. So on a sunny day your ISO can be 100, the minimum. Now the only way to stop overexposure is to increase the shutter speed.
In photography this usually isn't an issue (with the exception of some effects), but in video a fast shutter speed can make footage feel a bit choppy, because every frame is perfectly sharp.
you may think "what's wrong with it being sharp?" But acually in video a bit of motion blur makes things look smoother and more natural.
Ordinarily you can close down the aperture to reduce the light and shutter speed, but you don't have that option.
That's where ND filetes come in. They are essentially tinted lens covers, like sunglasses which reduce the amount of light coming in the lens. This allows you to slow the shutter speed, to allow motion blur, without overexposing the footage.
The rule of thumb often cited for appropriate shutter speed is about half your frame rate. Eg: @ 25 fps, 1/50 of a second. @ 30 fps, 1/60. @ 60 fps, 1/120, etc.

In stills photography you mostly want to avoid any motion blur, but in cases where you do the ND filers can be used. One common example is long exposures on waterfalls or waves. I'm sure you have seen those sort of pics.
Perhaps in sports you may want a tad of blur to give a dynamic impression of speed or movement.
So that's what ND filters do. It's totally up to you if you think you want or need them.

Sam654 Posted at 10-22 01:50
Because the Mini series drones have a fixed aperture, this limits the control you have over exposure.
In general photography/videography you will have three veriables for exposure, Shutter Speed, Aperture and ISO.
But on the Minis you only have Shutter Speed and ISO that can be altered.

Thanks for the info. really helpful

I have been flying drones for 5 years are rarely use ND filters, but use them all the time on my Lumix full frame camera.

I get frustrated with drone pilots who only seem to focus on using ND filters to get blurred motion, which, by the way is nebulous and pointless when you’re flying the drone at altitude in cinematic mode because there isn’t enough motion to blur.

ND filters have a broad range of uses other than to create motion blur - for example, in harsh light conditions when you’re not able maintain good exposure even at ISO 100 and high shutter speed; when you want to freeze the motion of something like a waterfall when taking a photo; or reduce the glare and reflections from water.

I use my ND filters for these scenarios BUT NOT to create motion blur. The reality is that unless you’re flying your drone (such as an FPV drone) at very high speed close to the ground or buildings there isn’t enough motion to blur in the first place.

Steph Jant Posted at 10-22 08:51
I have been flying drones for 5 years are rarely use ND filters, but use them all the time on my Lumix full frame camera.

I get frustrated with drone pilots who only seem to focus on using ND filters to get blurred motion, which, by the way is nebulous and pointless when you’re flying the drone at altitude in cinematic mode because there isn’t enough motion to blur.

It's true that ND filter have many more uses in the wider world of photography and video.
But here I focused on the specific reasons they are popular among Mini Drone users. Notably to get over the limitations of a fixed, wide aperture.
Whether someone wants/needs motion blur comes down to their particular use case  or creative preference. No one is saying must use them for that and that only. Like anything, it's another tool that's there for the times it fits your needs.

Hi, Potato mini. Thank you for reaching out. By choosing the appropriate filter, you can have more freedom to control the aperture or shutter, which provides more exposure options and space for your creation. They meet the needs of scenarios when shooting long exposure or in harsh lighting, e.g., long exposure timelapse. Hope this helps.

There are 2 reasons (simply put) to buy ND filters.
1 : long shutter exposures during daylight. For this you need high densities (1000 + ) and it is not often used on drones, but can create nice hyperlapses.
2 : getting the 'right' (slower) shutterspeed that introduces a bit of motion blur for video.
Now this does help a bit in certain situations, but it is not something I would consider as one of the first things to get.
There are (IMHO) more important things you can master (for free) which will improve your video much more.
- Learn how to tell a story with video
- Learn about compositions
- Learn how to make interesting movements that help you create nice video footage.
- Learn the camera techniques.
And then there is the last 5% that can be improved with ND filters

Montfrooij Posted at 12-6 11:39
There are 2 reasons (simply put) to buy ND filters.
1 : long shutter exposures during daylight. For this you need high densities (1000 + ) and it is not often used on drones, but can create nice hyperlapses.
2 : getting the 'right' (slower) shutterspeed that introduces a bit of motion blur for video.

that makes since. thanks for the help

Potato mini Posted at 12-6 12:47
that makes since. thanks for the help

No problem.