What does it mean to trip in PTC Fuses?
The hold current is what it's guarranteed to carry, while supplying the load as a fuse should, so with most of the supply voltage across the load. If your load takes 1A for normal operation, then your hold current must be higher than 1A.

In the normal untripped state, the resistance is low, and the heat being dissipated in the PTC is low enough that its temperature and so resistance remains low.

When it reaches trip current, the temperature exceeds a threshhold, and the PTC becomes high resistance. The current drops due its high resistance, which  removes most of the voltage from the load. As long as the supply voltage remains connected, the PTC stays hot enough to stay in that state.

You should choose a PTC with a trip current

a) Higher than your load will ever take, to avoid nuisance tripping
b) Lower than your power supply can deliver, otherwise your PTC may never trip.

A common mistake is to use a PTC with a trip current that's too high for the power supply. Under fault conditions, the PTC is then unable to trip, and the power supply cooks.

'Tripped current' is not specified for the PTC, it's the Pd, the typical power dissipated in the tripped state that's defined. The tripped current can then be estimated as Pd divided by the power supply voltage.