The jamb bracket was always loose, so I had to keep using longer and longer screws to make it stronger. Over time the wood completely got eroded, left with a gaping hole and no place to insert a screw. How do fix this? I have a young handyman who is painting my house and I was going to have him fix this, but I don't think he knows how. If someone can explain clearly I'm sure he can do it.
As Eric suggested, clean out any loose debris first. But do not use small pieces of wood such as toothpicks (they are usually made from very cheap, low-density wood, that easily crushes when you insert later the screw for the hinge). Get a wood filler (which consists of sawdust in a binder) and fill the gap flush. The filler has a much higher compressive strength than matches and toothpicks (around 400kg/cm2, or 5600 PSI). Then drill normally and fasten the hinge as you would with a new door.
Edit: regarding the comments below about brittleness, I personally recommend Abatron WoodEpox. I used it several times, and I can guarantee you can drill into it.
Edit 2: In their website they say it's designed to be able to drill into it. Source: https://www.abatron.com/product/woodepox/
Go to your home store and pick up a package of dowel pins or just get one big dowel rod and a drill bit to match.They come in many sizes depending on the hole you're trying to repair.
Drill out the eroded wood, squirt some wood glue in the hole and tap in the dowel pin and let the glue dry.
If you are going to use one long rod and cut it to the size you need, cut a small grove length wise in your pin to allow excess glue to escape. This isn't needed if you buy a package of dowel pins because they are already grooved. After the glue dries, sand and paint the area and then you can reinstall the jab bracket.
Plastic hole inserts.
I had the problem you describe, and kept fixing the growing hole with the toothpicks and glue method. Either because of the nature of the jamb wood or the weight of the door the screws would eventually get loose and I would need a longer screw or to refill the hole ... sound familiar?
I got some of these screw anchors. Bigger than the one depicted. They are mostly used for masonry or concrete to give the screw something to bite, but they worked great to fill the eroded holes behind the screw. I tapped them into place with a hammer. I think the plastic anchor absorbs the motion of the screw with use of the door and does not transmit it to the wood - so it does not cut / erode the hole bigger.
If the hole is too big for the anchors you find you could anchor the anchor with the described wood glue and many sticks method.