Q:

Why is Penny less concerned about the "check engine" light?

On many occasions in The Big Bang Theory we have seen Penny being questioned about the "check engine" light, especially by Sheldon Cooper and even by Beverly Hofstadter. So is there any significance or just Penny's carelessness?

A:

The check engine light is being used as an indicator of the relative difference in general concern by Penny versus Sheldon or Beverly.
The check engine light in modern vehicles quite often indicates an issue with the emissions control system, although as commenters have noted it can cover a wide variety of vehicle faults (including those unrelated to the engine).  Often these underlying issues pose no immediate danger to the mechanical function of the car, the initial symptoms of emissions issues being increased environmentally-harmful emissions and lower fuel economy.
Thus, many people ignore the check engine light, either after checking it once and finding out that the underlying issue is emissions-related or otherwise not immediately harmful, or in some cases never checking it at all.  However, there is always a chance that the problem is one that may quickly damage the vehicle, and the only way to know for sure is to have the error code checked by a mechanic (or checking it yourself if you have the specialized equipment).  In addition, a person who cares deeply about their environmental impact would want to fix any underlying emissions problem, not to mention the potential for long term damage if the light is consistently ignored.
Thus, response to the check engine light can show how careful a person is along a continuum from most careless to most careful:

completely ignoring it from the get go
having it checked the first time it is lit but assuming things are fine on subsequent lights
having it checked it every time it goes on 
not operating the vehicle until the underlying cause is solved

Sheldon and Beverly are both of the sort that is very concerned with minutiae, and Sheldon in particular has shown concern for potential issues of low probability but high potential impact.  Both are detail-oriented and meticulous.  Penny, conversely, lives a somewhat oblivious existence, relying on her ability to respond to situations rather than on extensive planning, care, or forethought.  Their responses to the check engine light are indicative of these personality traits.

A:

It is also implied, deliberately or otherwise, that she doesn't understand what the light is for. In Series 2 Episode 14 – The Financial Permeability, there is a conversation between Penny and Sheldon where the engine does inevitably break:

Sheldon: If you recall, I pointed out the “check engine” light to you several months ago.
Penny: Well the “check engine” light is fine. It’s still blinking away. It’s the stupid engine that stopped working. It cost me like twelve hundred dollars to fix it.

Quote Source

A:

It should also be noted that Penny is a waitress and doesn't really make much, for regularly maintaining a costly possession like a car.
So, she doesn't care about the car's condition unless and until the problem is a major, like the one pointed out by @MatthewSteeples.  In Penny's words:

Sheldon: If you recall, I pointed out the “check engine” light to you
  several months ago.
Penny: Well the “check engine” light is fine. It’s still blinking
  away. It’s the stupid engine that stopped working. It cost me like
  twelve hundred dollars to fix it.

So, a sensible inference to make is that even if she knows what the light is or, she can't/doesn't really care to repair it as she cannot afford minutiae servicing (which can cost a lot for a car).
In addition, Penny represents most (American) common people. And most people don't really care about the environment unless it is directly spoiling our health or is costing us a lot. Thus the reluctance of Penny towards servicing the problem.

