Java
Let's start with the confusing part: You can develop software using Java, JavaScript, and Enterprise Java Beans. These are three different systems that are related mainly by the work "Java" in their names. Of the three, Java is the one you'll see in mobile development, so let's start there.
Java is an object-oriented programming language developed at Sun Microsystems. It is now owned, along with the rest of Sun Microsystems, by Oracle. It is, by most accounts, one of the most frequently used programming languages around, so the skills are available in many individuals offering their services to enterprises. That's very good news.
More good news comes from a performance standpoint. Java is a compiled language that can be run in two different ways: either in a browser window or in a virtual machine that doesn't require a browser. That flexibility tends to mean a lot when it comes to re-using code and updating software.
If you're looking at Android as your primary platform you’re almost certainly going to look at Java. If iOS is your main target, you probably won't be doing Java-first development. And if you want to develop a common code base that runs across many different platforms, then Java should certainly be on your list of finalists.
I mentioned that we were starting with Java. A quick note on JavaScript: It is, as the name implies, a scripting language for Web browser apps. It can be useful for adding features to a Web page, but isn't, by itself, the solution you're looking for when it comes to mobile app development. Keep it in mind, though, if you're walking down the HTML5 path.