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Stage 1
These are modifications that can be performed in isolation. For example: changing an air intake, changing the type of brake rotor (from solid to grooved or drilled for example).
They often don't provide large performance increases (either in terms of power/bhp, or in terms of handling), but they are also usually the cheaper types of modification that can be performed, when compared to those "classified" as stage 2 or 3 modifications.

Stage 2
These modifications are usually larger, more complex modifications, that usually more work than just "bolt it on", and often require additional parts or modifications to be in place before they can be.
A good example of a stage 2 modification may be the inclusion of a supercharger on a naturally aspirated vehicle, as whilst the charge could in theory just be bolted on, it will also require the ECU to be "flashed" or replaced, as well as an air filter upgrade, and maybe even new injectors.

Stage 3
Stage 3 modifications are often the most complex and could be termed "track day" modifications.
Like stage 2, they almost always require other modification to be in place before they can be performed, but also quite often make the target vehicle less than ideal to be used on the road.
A good example may be the switch to an aggressive cam profile, which would provide great benefits on a track, but would cause issues in stop-start morning traffic commutes.