1. An informal, colloquial greeting (a contraction of "how do you do?"). Primarily heard in US. Well hey, Bob, howdy-do? Been a long time since I've seen you around here!
2. An unfortunate, unpleasant, or awkward situation or circumstance; a troublesome or difficult state of affairs. (Often phrased as "a fine howdy-do.") Primarily heard in US. Well that's a fine howdy-do. I'm on the job for just two days and I find out that the company is going bankrupt!