But what exactly this Avijja? Improper attention, ignorance?
Its "ignorance" or "not-knowing"; as defined in the suttas. Its not "improper attention". "Improper attention" is attention polluted by ignorance. Compare this to water polluted by poison. The poison is one thing & the water is another thing. Similarly, the ignorance is one thing and the attention is another thing.
What are we ignoring, and then what's the fact that we should not ignore or we should look in the world?
It does not mean "ignoring". It appears you read "ignoring" on another answer, which was a wrong answerused the word "ignore" incorrectly.
How can we uproot it?
It is uprooted by insight (vipassana).
I know Avijja can be easily answered in few words
It appears you do not "know". It is best to not say: "I know". "Ignorance" does not mean "ignoring". It does not mean "improper attention". Therefore, it is best to not claim "I know".
(e.g. with definitions, or some other synonyms) -- but why I'm asking this question is, it says that uprooting Avijja is the path to Enlightenment.
If someone "ask how to be a mathematician?", an answer would be (I'm limiting the answer set in a way to explain the question), "you need to learn addition / subtraction, integration, differentiation, etc." So what I'm asking is like "how to be enlightened?", an answer is "uproot the Avijja".
The above is illogical. To be a mathematician requires to learn addition / subtraction, integration, differentiation. To enlightened requires to learn four noble truths, three characteristics, dependent origination, emptiness, etc. We cannot say merely "uprooting ignorance".
So now I'm asking "what is Avijja?" like "what is addition?".
Ignorance is defined in the suttas as not knowing or not understanding the four noble truths & the three characteristics.
Please I just try to explain the answer with these stories, but not to offend anyone. With Metta, I'm expecting a detailed answer from the wise people in the community.
I am a wise person in the community. Study my answer if you are also wise.