The alternative is tweezers. There's a few really annoying problems:

It's very easy to squeeze a bit too hard or not quite get the grip right and the part will ping off and you'll never find it.

If the tweezers get a bit of solder paste on them the components start to stick so you can't let go of them.

It's really hard to get the components out of the tape - so you tend to have to tip them out and then they are upside down so you need to flip them over. Which is really hard with tiny components and again you often lose them.

For larger components (e.g. MCUs) its quite hard to pick them up in a way that is easy to place with tweezers.

To add a little to the existing replies. When you buy surface mount parts, they normally come on tapes - little plastic/cardboard strips with indents that the components sit in and a film over the top. These tapes are sold as reels if you need lots of units, but most hobbyists buy "cut tape" which the big distributors offer.

In a production setup, the pick and place machine accepts the reels and uses a vacuum tool to pick the parts up. It knows the orientation of the part in the tape (which is fixed) and where it needs to go on the board. Often components with irregular tops (usb connectors for example) will have small piece of kapton tape fixed to them to aid pickup. This is important: if you're doing this with tweezers, it's often annoying to pick the parts out of the tape and if you dump on the table you usually have to flip things the right way up, rotate them, etc. So a vacuum tool makes that a lot easier.

Small pens already exist and so do diy options like aquarium pumps, but this is a really polished looking project and great if it's open source too.

I once replaced a faulty SMD fuse on a laptop motherboard; I used tweezers and a microscope. Could I have done such a repair with a pick and place theoretically?

Got it. Thank you for the additional insight!

This is used for circuit assembly indeed. The vaccum is used to pick a small component from a tray and place it on the PCB at the right place. As the components are so small nowadays the small tip of the nozzle helps where human hand would be to big.

Placing large chips with tons of pins on a circuit board that has had solder paste applied needs precision to get it in the exactly right place.

Can't do it with just forceps, which are fine for smaller parts.

They tend to jump into place thanks to the soldier surface tensions so you don't need to be exactly right.

It's just more convenient using this.

It is less about them jumping and more about it even being possible to use forceps to begin with to place them without disturbing pins or paste.

For example TQFP-144 and fBGA256 parts are hard to place with forceps alone. Let alone larger parts.

Smaller parts are so much easier with a vacuum pen. You just need expensive tips for 0402 and smaller.

I tried Aliexpress but all I get is "adult massage toys"

The phrase may be "pick and place" along with vacuum