The Romans had a different perception of gods than we do. To them a god was powerful, but by no means omnipotent, an entity with which to negotiate - the Romans swore to a god, for example, that if a friend safely returned home, they would give a sacrifice to that god. Due to this, it can be said they thought of their gods as immortal and far more powerful duoviri ( mayors).

As for emperors, the quote from the historian Mary Beard sums it up perfectly:

Many Roman emperors became gods. That process was a complex one, and it took different forms in different parts of the Roman world, at different periods and on different occasions. Sometimes the Roman senate would officially declare a Roman emperor a god at his ‘death’, and would grant him a temple and priests. In some provinces religious worship of the emperor during his lifetime was the central way that loyalty to Rome was expressed. Sometimes the emperor would merely be likened to a god, given honors that were ‘equal’ to the gods, but not exactly the same. None of this is quite as crude (or silly) as it is often painted. In Rome the division between humans and gods was seen essentially in terms of power. There was almost bound to be a debate about where on that spectrum the all-powerful single ruler of the Roman world belonged. Or, to put it another way: if gods could be treated rather like overblown duoviri, then the infinitely more powerful emperor could, or must, be treated as a god.

As for your precise question, yes, those involved in politics thought it an honorific, but to the average Roman it meant that if he liked the late emperor he might now pray to him