It means they have poor pass rates. That means they are going to be weaning out students at a higher rate because they aren't going to want people sit for their boards if they are concerned they might fail .
If the nursing program I really want to go to is under warning by the BON, how serious is that? Should I be hesitant to apply?
Oh yes. You should run away quickly from this facility. Contrary to publicity, there is NO actual nursing shortage at this time. There are TONS of nurses out there applying for positions. Graduating from a non-accredited facility will only serve to put your resume in the first-out bin in a highly-competitive market.
There is a school in my area that is in that position right now. I know some people that go there, and let me tell you. After talking nursing to them, I can see exactly why they are not passing boards!!! It is so scary. I would never want one of them as my nurse! Find somewhere that has a good reputation. It will help you in finding a job. Trust me, HR is aware of when a school is having these problems....usually everyone knows..
You should probably look at their NCLEX pass rates for the past few years and see if it is a trend or a one time problem. If they are at all interested in saving their program they are probably working pretty frantically to clean house.
The last thing you want to do is sign on to a school that could be closed in a few months.
This happened at a school near mine - most of the current students frantically came to my school to try to sign up and save their schooling but a) Our nursing school does not transfer nursing credit in from that institution and b) my school was a lot more strict about who they let in.
This is your money, your time, your degree, your career. Don't leave it in the hands of a school that quite obviously isn't doing well.
Yes, you should be very hesitant. Even if you're able to finish their program and pass NCLEX, if they're "under warning" by the BON it's probably not a secret and their reputation is probably not very good with local employers. That, as roser13 astutely points out, will lead to incredible difficulty with landing a job. Run, don't walk, away from this place as fast as you can.