One way to hold this phrase is a line of people waiting, with one of them standing at the front where everybody can see. The word apparent is doing the work: it means the position is already out in the open, not something to be decided later. Nobody joining the line afterwards can step in front. That picture started in royal families, where the law made it true, and English later lent it to any place where one person clearly stands at the front of the line.
From the word’s history
From Middle English heier apparaunt, a word-for-word translation of Middle French heritier apparent. French puts the describing word after the noun, and English kept that order when it borrowed the phrase, which is why apparent stands behind heir. Apparent here means open to view, already plain: the right is not in doubt.
來自中古英文 heier apparaunt，是照著中古法文 héritier apparent 一個字一個字翻過來的。法文的形容詞放在名詞後面，英文借的時候連語序一起搬走，所以 apparent 才站在 heir 的後面。apparent 在這裡的意思是「擺在明面上、看得出來」：這個繼承權沒有懸念。
Wiktionary, "heir apparent"
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