Showing research experience in graduate applications As an undergraduate, I have heard this term a lot. I have not graduated but will graduate soon.

When applying to graduate programs, research experience is what everyone tells.

Research Experience is used rather recklessly. Many students, even if they had to just type in data for professors/researchers, check some test tubes in laboratory or whatever depending on discipline mention they had research experience.

Last year, I had an internship at a renowned research organisation. The only thing they do is research and development. As an intern, I did not specifically join saying, I wanted a "Research Experience". I were involved in their project which was a research project. My task consisted of API development, working with Matlab and various stuff important for the project. 

Yet, I did not come up with something new. Well, they did.

So, this is far better than what many students mention as research experience. But, is it worth calling this a research experience in my CV or applications? Shall I call this reaserch?

Making the question specific, what does a "Standard Research Experience" consist of? When graduate schools say undergraduate research experience, what kind of activities are they expected to have been involved in?
You're expected to describe research experience. It sounds like you've had some. You should describe it in your application. Talk about what role you had, what sort of things you actually did ("various stuff important for the project" and "working with Matlab" aren't very good descriptions). What was your role? Did you make decisions or did you just assist? What sort of products did you produce and what skills did those products require? How did you solve problems you encountered?

The idea behind these application questions is to try to differentiate people with no experience from some minimal experience (cleaning instruments in a lab and feeding rats) to moderate experience (sounds like what you have) and people who engaged in truly independent research (which is pretty rare, depending on where you did your bachelor degree and in what field). Be honest and detailed, that's all that's expected. Of course people will play up what they did, but if you made substantive contributions that demonstrate your abilities and experience, that will show through in your write-up.