Majestically is how something moves or appears when it is majestic: slowly, grandly, as if it has all the time in the world and knows it looks impressive. An eagle circles majestically; a ship comes majestically into harbour; mountains rise majestically from the sea. It is the adverb of majestic, so it tells you about the manner, not the thing itself. It is a little literary; in everyday talk people more often use the adjective (What a majestic view) than this adverb. Use it when the movement or the way of appearing feels grand, not only the object.