I really don't see any deep significance to these verses, which begin the story of Samuel, who is to become the judge and true ruler of Israel—a central figure in the reigns of Saul and David. As is often the case in traditional scripture, such a hero-to-be is given a somewhat miraculous birth (Isaiah, Samson, and so on). Hannah is barren, "the Lord had closed her womb." In subsequent verses she will promise the Lord, in the presence of the priest Eli, that if she gives birth to a son she will dedicate him to serving the Lord "all the days of his life." Of course, she subsequently becomes pregnant and gives birth to Samuel, who is indeed dedicated to the service of the Lord.
I think the message is the same for us. If we feel our lives to be blocked in any way, we must stop trying to deal with the challenge through ego mind insistence on 'knowing what we know' and surrender it instead to the Presence of the Divine within, always available to make smooth our way. And if we intend our goal to be in service to Truth, we can be sure we will achieve it.