He means he doesn't take his allocation of days away from work but instead he sells those days back to the company.

Why is that good? Beats me. Unless he gets an above average holiday allowance it sounds terrible both for his long term health and for his productivity.

It means I don't use all my allotted off time and I take part of it as pay at the end of the year. In other words, I am reliably in the office. This is considered important where I work and taking more time off than you are entitled to can be grounds for being fired. Promptness and being on time are also valued by the company I work for and deemed indicators of reliability -- are you there when they need to ask you to do something above and beyond your normal daily duties?

As for other remarks made here:

I mention it first in part because a coworker likely was recently fired in part because they were routinely late and, after strolling in the office late, would then mosey down to the cafeteria and grab a bite to eat. I don't know for a fact, but remarks that were made suggest to me that this employee generally failed to do the quantity and quality of work they were expected to do. I think the experience at my company is that tardiness and abuse of time off usually correlate to poor work performance.

I am not actually sacrificing my health by working the hours I do. My health has steadily improved in the three years I have had this job. I don't really understand the whole idea of "taking a vacation" and I never have. But that's probably something I can't adequately explain to most people.

I'd guess he means not actually going on a holiday but "taking" your holiday in the form of additional pay instead.

It could be thought of as an indication that the employee in question is a dutiful little peon, which some bosses would probably like.

On the other hand, if someone tried to do this in Finland in July, when practically the whole country is on summer holiday and workplaces are very nearly totally empty, it might not work that well.