Emily Dickinson has a very distinct style of writing, and unusual capitalization is just one of the facets of that style. The reason that she probably chose to capitalize certain words was to give them more emphasis or importance. Dickinson wrote really short, dense, minimally worded poems, so she had to make every single word count. If she capitalized a word, it gave that word an extra punch of power, without having to add more words, or explain herself.
In the poem "Will There Really Be a Morning," if you look at some key capitalized words, and think about what purpose is served by those capitals, it can help you to understand her style a bit better. Here are the words that she uses unusual capitalization with: "Morning", "Day", "Water lilies", "Bird", "Scholar", "Sailor", "Wise Men", and "Pilgrim". Her entire poem is wondering whether or not morning will come, and if day really exists. She wishes she could see it come before anyone else, and wonders where it does come from. So, since morning and day are such huge issues for her, she capitalizes them. It gives morning and day more royalty, as if she is making them a person, and giving them supreme importance. At the end, she is appealing to anyone who can give her answers, and respectfully capitalizes those she appeals to. She asks if there isn't a scholar, sailor or wise man that can answer her question. Capitalizing those gives them ultimate respect, and endows them with wisdom and authority. And, since she is appealing to them for wisdom, her capitalization fits there; she is humble and ignorant, and is supplicating their wisdom. Capitalizing those titles shows subservience and a willingness to listen. So, in this poem, her capitalization shows reverence for wise people, and a salutation to the important topic of the poem. I hope that those thoughts help; good luck!