Is MOSFET threshold min and max only limits when it goes on and off?
It is guaranteed to pass less than or equal to 250uA with 1V on the gate and drain.
It is guaranteed to pass more than or equal to 250uA with 2.5V on the gate and drain.
250uA with 2.5V across it is about 10K equivalent which is not very much 'ON'.
If you want it to be guaranteed to pass a useful amount of current greater than 250uA (like, say 50mA with a fraction of a volt across it) you will have to give it significantly more than 2.5V
How much more can be guessed at from the curves (such as figure 1), but the only datasheet guarantee is that it will have less than 5 ohms resistance with 10V on the gate, passing 0.5A, when cold, or 9 ohms when very hot.
'Typical' is what you might expect an average unit to do if you pick it off the assembly line. They don't guarantee it, it may not be valid, but usually (sometimes) it's pretty close. If you want to build many units and have all of them work reliably and over a wide temperature range and component tolerances you don't pay much attention to 'typical' numbers.
Think of it like ordering piece of lumber at your local big box store. It's nominally say 3' (1m) but it might be an inch (25mm) shorter or longer than that. Semiconductors are not individually trimmed (cheap ones anyway) so you have to live with the tolerance from the manufacturer. If you absolutely need a 3' (1m) piece to fit you'd better order it longer and cut it down.
In the same way you might want to use a 2.5V rated MOSFET* for operation at 3.3V because it has guaranteed characteristics that apply at 3.3V.
* by this I mean the Rds(on) is guaranteed with Vgs=2.5V.