All development is done using your choice of C#, Boo, or a dialect of JavaScript.
C# needs no explanation 🙂
Boo is a CLI language with very similar syntax to Python; it is, however, statically typed and has a few other differences. It’s not “really” Python; it just looks similar.
The version of JavaScript used by Unity is also a CLI language, and is compiled. Newcomers often assume JS isn’t as good as the other three, but it’s compiled and just as fast and functional.
Most of the example code in the documentation is in JavaScript; if you poke around the official forums and wiki you’ll see a pretty even mix of C# and Javascript. Very few people seem to use Boo, but it’s just as good; pick the language you already know or are the happiest learning.
Unity takes your C#/JS/Boo code and compiles it to run on iOS, Android, PC, Mac, XBox, PS3, Wii, or web plugin. Depending on the platform that might end up being Objective C or something else, but that’s completely transparent to you. There’s really no benefit to knowing Objective C; you can’t program in it.
Update 2019/31/01
Starting from Unity 2017.2 “UnityScript” (Unity’s version of JavaScript, but not identical to) took its first step towards complete deprecation by removing the option to add a “JavaScript” file from the UI. Though JS files could still be used, support for it will completely be dropped in later versions.
This also means that Boo will become unusable as its compiler is actually built as a layer on top of UnityScript and will thus be removed as well.
This means that in the future only C# will have native support.
unity has released a full article on the deprecation of UnityScript and Boo back in August 2017.
As far as I know, you can go with c#.
You can also use the obscure language “Boo”. (Found at https://boo-language.github.io/)
In the past (before about 2012) it was possible to use a strange variant of Java but that is now deprecated and does not work.
Note that Unity builds to Android / iOS, and many other platforms. The fact that iOS programming uses objective-c or Swift, is, completely irrelevant at the Unity3D level. Unity is programmed using c#.