It means that a person worked 14 hours each day, in a week's time. From your sentence, I don't know how many days exactly. A typical week is 5 days (with two rest days) but some people do put in 7-day work weeks.

I think that "a week of fourteen-hour days" refers to a week, where a person has to work 14 hours a day for 5 days. *Could be 7 days, but that depends on the kind of job. Most rig workers work 14+ hours a day for 2 weeks.*

If it's about a job, it means for the working week, you work 14 hours each day. Gruelling.

Are you referring to 'one' week or each week?