Objective-C is, in a sentence, the programming language used to build applications on Apple platforms, including the iPhone and iPad. Your graph coincides nicely with the rise of the iPhone and iPad among end users. There is no other language available for iOS; programs not written in Obj-C, even if they run on the hardware, will not be accepted by Apple for download from the Apple Store. So, if you want to program on the most popular single mobile platform in existence, you program in Obj-C.
Java/C#/C++ didn't have the same boost (or to the same degree) that Obj-C did because those languages were already popular with the "open-architecture" community (those programming for platforms other than Apple's; before the iPod rocketed Apple back into relevance, its computers were only 5% of the market share of personal computing devices). Just last year, Java, C, and C++ in that order were the top 3 languages:
- Java is #2 on mobile devices behind Obj-C, and has a sizeable chunk of the Internet, with JSP/Servlets being a popular code component of web stacks (especially Linux-based stacks such as JOLT/LAMJ).
- C is the grandaddy of them all; it's one step from assembler, and as such there's a compiler that'll get you from C onto pretty much any chip ever made, including the ones behind most of the game consoles all the way back to the Sega Master and 8-bit Nintendo systems. This close-to-the-metal approach is also key for performance-critical applications like device drivers, kernels, graphics, etc.
- C++ is "C one better", and like its predecessor is highly standardized and will compile onto almost any chip ever made, but also usually requires a specific runtime or library set that was targeted. As such it's not quite as portable, but you see a lot of desktop applications, including PC games, written in C++ and targeting either the Windows or Linux runtimes.
Compared to these pedigrees, Objective-C's is extremely limited; it was developed in the early '80s as a thin layer of SmallTalk-based object-oriented features over otherwise ANSI-compliant C, and picked up by Steve Jobs' new startup after leaving Apple, NeXT. It didn't see real adoption into a major platform until Jobs went back to Apple (bringing NeXT with him), and subsequently used NeXT's OpenStep and AppKit (and thus the Objective-C language) to build OSX. The language saw stirrings in the consciousness of the developer community with the launch of OSX Leopard (which targeted Intel CPUs), and then its rise to global prominence with the launch of the iPhone, and the subsequent "there's an app for that" commercials showing all the things it could do. That sparked huge consumer demand, in turn fueling demand for this language that prior to 2009 seemed destined for obscurity among a handful of Mac developers, most of them working for Apple.