Words like 'boom', 'bam', 'zap', 'bingo' ... can be used as nouns and verbs in normal sentence constructions, but in your example I would call 'boom' an interjection because it is an extra word being inserted into a sentence that evokes or describes an emotional response. You could leave it out and the sentence would still make sense. The interjection is a more descriptive way of saying 'all of a sudden' or 'suddenly'. A few similar examples: I was rewiring this bad outlet when, ZAP, a jolt of electricity ran up my arm. She was wracking her brain to remember his name when, bingo!, it came to her. We saw Brad whisper something in her ear and WHAP!, she slapped him across the face. Since this is informal English writing, the use of punctuation and capital letters is up to the writer. In your example, it seems like the word 'boom' is not really a big 'BOOM' anymore ... just 'boom'. He met her, it's over-and-done-with, he's moving on -- so the quiet 'boom' reflects the change from initial surprise to his current 'oh well' attitude. No need to make the word stand out in any way.

It means that he ran into his ex-wife. Think of boom as all of a sudden or suddenly, like an explosion. And "it happens" is making reference to the previously established action: "running into your ex-wife".