stkroot, The auxiliary "will" can express the future, desire, willingness, polite request, etc. Future The train to Liverpool will depart from Platform 7 in ten minutes. Desire I will have a hamburger and a coke. = I want a hamburger and a coke. Willingness Will you marry me? = Are you willing to marry me? Yes, I will. Will you take care of my dog while I am on vacation. = Are you willing to take care of my dog while I am on vacation? They bank won't lend me any money. = The bank isn't willing to lend me money. Request Will you get me a hamburger and a coke please? = Please consent to get me a hamburger and a coke. Will passengers please board the train now. = Passengers, please agree to board the train now. I suggest you use an Advance Learner's dictionary such as The Merriam-Webster Advanced Learner's Dictionary, or the Oxford Advanced Learner's Dictionary. These dictionaries answer the simple questions about usage and provide many examples.

"Will" is being used to form a third person request. You will hear "will" used this way in authoritative announcements. Another example: "Will the person who lost their glasses please see Jill at the front desk?" (announcement by company receptionist)

The second sentence is a question and should be written "Will passengers please board the train now?" Let's examine the simpler sentence: "Will passengers board the train now?" Taken literally, the word "will" makes it a question about what the passengers will do in the future. Question: Will the passengers board the train now? Answer: Yes, they will board the train now. OR Person B: No, they will not board the train now. When we add in the word please, it lets the listener know that the speaker hopes the answer to the question is affirmative. "Will the passengers please board the train?" means the same thing as "I want all of the passengers to board the train." In other words, the construction "Will please <do something>?" is a polite way to request that <do something>.

In this sentence it means, 'is going to'.