What does a delta E tolerance of 2 actually mean?

It means the printed colour must sit within two CIEDE2000 units of the agreed target when measured, which is a difference most observers would struggle to see side by side. Delta E is a measurement, not an opinion, so it only works as an acceptance criterion when the target values, the measurement conditions and the formula are all named in the specification. ISO 12647-7 shows the approach in practice by fixing numerical limits for a contract proof.