Herc, So many different boiler programmers/clocks/timers out there, but here is the likely explanation.
ON the boiler will stay on 24 hrs. and will only shut down when the various thermostats are satisfied.
CONSTANT the boiler will stay on between the first time setting you have programmed e.g. 06:00, and the very last setting of the day you have programmed e.g. 22:00.
TWICE A DAY allows you to set morning times e.g. 06:00 to 09:30, and a evening time e.g. 17:00 to 22:00.
OFF is self explanatary.
There will probably be some indication re manufacturer,Danfoss,Honeywell etc. you should be able to request a user's guide.
Hope this helps.