I thought about one of those odd little cases in English of a word having two very common but seemingly quite different meanings. I was watching something in which someone convicted of a crime mentioned making an appeal, when I wondered: why can we also say that something is appealing to us?
There might be no obvious link at first glance, but if you think about French, it might start to make sense.
The verb to appeal comes from the Old French apeler (same meaning), which comes from the Latin appellare, which also meant appeal, but meant to accost, address, summon, and name as well.
For me, it’s that last meaning that provides the major clue. Think of how you say My name is…. in French: Je m’appelle…, literally I name/call myself.
So if you make an appeal to someone, you’re effectively (and perhaps quite literally) calling on them to help you.
And if something appeals to you, it’s like it’s calling to you, attracting you to it.