What does 的 mean in 表示对某人某事的亲近和关心?
表示 (v) = to indicate /to show / to express
对某人某事 = toward some person or something
&quot;对某人某事(的)&quot; = &quot;(of) toward some person or something&quot;
的 functions as an adjectival suffix here. The whole phrase &quot;对某人某事的&quot; is now an adjectival phrase for the object &quot;亲近和关心&quot; (fondness and concern)

[表示] [对某人某事的] [亲近和关心。]
[to express ] [the fondness and concern] [toward some person or something]