Translation:It would be nice if the public understood us.
It can mean that, but not in this case. "Ci" is locative, and it can mean "about it", "on it", "in it", and so on; in many cases the difference in English is trivial, e.g. "ci ho provato" and "l'ho provato" both mean "I tried it", but with different nuances (the first is closer to "I tried my hand at it"). In this sentence "capire" is transitive and needs a direct object, so "if the public understood it" would be "se il pubblico lo capisse".
I think that "ci" only means each other when the subject is "we" (either an explicit "noi", or a first person plural verb form). I think that for "each other" with "they", you'd just use the reflexive: "si capiscono" = "they understand each other". Here's an example in an Italian newspaper headline: http://gazzettadimantova.gelocal.it/cronaca/2013/10/31/news/dite-loro-avete-perso-1.8025891
I'm not a native speaker, so I welcome any corrections from passing experts.