In my background, the meaning (in a dojo setting as opposed to in common use in Japan during daily activities) has been explained to me like this. Onegaishimasu = "Please, would you train with me?" Along with this invitation to do something together is an implied agreement that we'll do our best to do this as well as we can and take care of each other.
Juniors usually ask the senior and the senior nods or says something that acknowledges their understanding of the agreement.
This has been explained to me by several senior budo teachers in similar ways but the capsulized version above is mine.
I have heard many other interpretations over the years. I'm always curious to hear more...