meaning - What does "wax lyrical" mean in this context?

The idiom wax lyrical means to talk about something with a lot of enthusiasm.

There are similar idioms, like wax eloquent (talk about something eloquently), wax poetic (talk about something in flowery speech) and wax wroth (talk about something angrily or with agitation).

Lyric comes from the classical instrument, the lyre. The word was transformed via old french to mean a "short poem expressing personal emotion". Wax means "to grow". So literally it means "to grow in poetic and emotional speech", but usually the phrase just emphasizes the interest and excitement the speaker has for the topic.