I’m fairly sure that “inauguration” is only a spelling word for so many American schoolchildren because of its political associations. Likewise, I’m sure that most Americans hardly ever use it—usage probably spikes every four years, in January, and then probably fades out again.
The verb form is inaugurate:
1. to induct into an office with suitable ceremonies.
2a. to dedicate ceremoniously; observe formally the beginning of
2b. to bring about the beginning of
The word comes from the Roman practice of augury, which we more typically today call divination or (even more plainly, fortune-telling). This particular form was based on the flight of birds, and was one of variety different divination methods employed by the ancient Romans. The word augur itself is thought to have its roots in aug (“to increase; to prosper”). As in, it was a way to find out how to increase the nation’s good fortune and how they could prosper.
If an important action was to be undertaken in Rome, including ascensions to new political positions or some general public enterprise or project, an augures publicii was consulted in a ceremony of pomp and circumstance.
Today, in the United States, we keep the pomp and circumstance of inaugurate but not the superstition. Instead, the word has retained a sense of “first” and “beginning.” Curiously enough, without the in- prefix, augur still retains its divination-related meaning:
1. to foretell especially from omens
2. to give promise of; presage
So watch the birds today, during the Presidential inauguration, to see if they augur anything good.