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The Mars Exploration Rover (MER) Opportunity landed on Mars on January 25, 2004. The rover was originally designed for a 90 Sol mission (a Sol, one Martian day, is slightly longer than an Earth day at 24 hours and 37 minutes). Its mission has been extended several times, the machine is still trekking after 11 years on the Red Planet.

How it has been working for 11 years? Can anyone please explain how smart this rover is? What AI concepts are behind this?

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    $\begingroup$ Hardware-related aspects of "How it's been working for 11 years" are not within the scope of this site, except insofar as that relates to AI. Please edit the title and question accordingly. $\endgroup$ – NietzscheanAI Sep 13 '16 at 7:11
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The Mars Rover is a highly successful example of the 'New AI' that emerged from work by Rodney Brooks in the 1990s.

In a quote from Brooks:

In 1984 I joined the faculty at MIT where I have been ever since. I set up a mobile robot group there and started developing robots that led to the Mars planetary rovers.

Together with the 'Allen' paper, the foundational AI articles in this area are:

Although Brooks initially had difficulty getting this work published, preprints were widely circulated within the AI community. Brook's "Physical Grounding Hypothesis" (essentially: "intelligence requires a body") has now largely supplanted the preceding symbolist approach.

The capabilities of the MARS Rover are organized in a Subsumption Architecture. Rather than maintaining an integrated and complex 'world model', increasingly sophisticated behaviors are stacked in hierarchical layers. For example, 'walking' is a relatively low-level competence, with 'avoiding obstacles' and 'wandering around' being higher-level ones.

Layers in a subsumption architecture

Each layer is represented by a Finite State Machine that reacts to stimuli appropriate to that level. The activity of lower levels can be suppressed ('subsumed') by higher level ones.

Here is a schematic of the bottom two layers of 'Allen', Brook's first subsumption robot:

Layers for obstacle avoidance and wandering

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There is an interview (link see below) with David E. Smith, a senior researcher in the Intelligent Systems Division at NASA Ames Research Center. In this interview, he talks about the application of AI and AI planning in particular in his work at NASA. He also (just shortly) mentions the Mars Exploration Rover and cites related scientific papers (just search for "Mars").

Link to the official publication at Springer:
http://link.springer.com/article/10.1007%2Fs13218-015-0403-y

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