Hi guy,
Well I do not know if the term "high gain antenna" has ever been defined as such. What you usually have is a matter of one antenna having MORE or LESS gain than another type.
An omnidirectional ant. like a verticle or a ground plane can have gain in the frequency range which it is designed for and will receive equally well in all directions. To achive substantially higher gain, you will need to use a multi-element beam type antenna. With these, the more elements they have, the more gain you get. These are directional antennas which you put on a rotor so you can turn and point it at a given scanning target.
Then, you can do more by utilizing an electronic preamplifier or [ preamp ]for short, which will boost the incoming signal strength. But these devices will also increase noise and if you're in an RF rich environment, like near a big city, it usually will increase the likelihood of suffering instances of receiving intermod which is unwanted interference from strong signals on frequencies nearby to the one which you are targeting, yet these strong outside signals "overpower" your receiver's ability to reject or filter them out.
You will also get maximum efficiency and effect from a preamp if you select a mast-mounted type which connects right to the output connector of the antenna and requiers a power line run to it.
As to your wanting to reliably recieve traffic from 250 miles away....well good luck friend. That's pretty far. At those distances you are approaching or in fact going over the horizon. Ground wave radio signals, which is what you are "working" when you are talking about typical scanner frequencies ( VHF & above ), are only viable for line-of-sight operations.
But it can be done. Buy a place on top of a mountain and get a big beam antenna like 17 elements or more and a rotor and a high-end receiver....and then point that at your target.
You will also have to be mindful of other services, counties, departments....whatever it is you are wanting to listen to....may also be using this same frequency and you will hear more than one user occupying this same frequency in different locations.
So having "big ears" may or may not be a good thing...or too much of a good thing if you will. Again, depends on what you are trying to specifically accomplish.
Hope this info is of some assistance to you.