I have heard a lot about Ludwig Wittgenstein, but what are his greatest accomplishments? I tried looking up on Wikipedia but didn't understand much.
Well, if by greatest, you mean what is he renowned for, then certainly he is known for his Tractatus Logico-Philosophicus and his Philosophical Investigations written about 30 years apart. In fact, the change in the philosophical content is so stark, it's common to hear of him spoken as early and later Wittgenstein.
While it's not possible to give much detail to his ideas, there are some articles in both the Internet Encyclopedia of Philosophy and the Stanford Encyclopedia of Philosophy that touch upon his influence; and Wittgenstein is a giant of twentieth century philosophy.
First, you can read yourself some of his life and accomplishments here:
Early Ludwig is renowned for his logical atomism developed with Bertrand Russell. The condensed notion is that he and Russell influenced the philosophy of language heavily after Gottlob Frege and that the two men, as well as a few others attempted to create a systematic exploration of logic in natural language by presuming more or less there were atomic facts about the physical world that reflected the state of affairs. Perhaps presaging the logical positivists, and certainly influencing them, Wittgenstein continued a long tradition of defending a correspondence theory of truth. According to WP on logical atomism:
The theory holds that the world consists of ultimate logical "facts" (or "atoms") that cannot be broken down any further, each of which can be understood independently of other facts. Having originally propounded this stance in his Tractatus Logico-Philosophicus, Wittgenstein rejected it in his later Philosophical Investigations.[b]
Later Wittgenstein is very much a different beast, and certainly a hero in the philosophy of language both for his views on ordinary language philosophy (IEP) and his work laying the ground work for language-games and family resemblance. The former asserts that meaning doesn't inhere to the syntax of the language so much as the meaning the agent assigns to it. The latter attacks the notion that word definitions that are crafted with terms of sufficiency and necessity are adequate. Later philosophers of language like Elanor Rosch went out to posit theories such as prototype theory that suggests mechanisms of definition far more sophisticated that set-theoretic set-builder notation. Lastly, later Wittgenstein is famous for his notions of private language (IEP). From "Private Language Argument (WP)":
The private language argument is of central importance to debates about the nature of language. One compelling theory about language is that language maps words to ideas, concepts or representations in each person's mind. On this account, the concepts in one's head are distinct from the concepts in another's head. One can match their concepts to a word in a common language, and then speak the word to another. The listener can then match the word to a concept in their mind. So the shared concepts, in effect, form a private language which one can translate into a common language and so share. This account is found for example in An Essay Concerning Human Understanding, and more recently in Jerry Fodor's language of thought theory.
While being a seminal figure of logic and the linguistic turn, he had other ideas and contributions. Of course, Wittgenstein had other publications and other arguments, so it might be worth your time to read the following:
You should watch a 1993 movie called "Wittgenstein". I am not sure what exactly you mean by an 'accomplishments'. Most philosophers (especially analytic philosophers) would agree that he was the greatest philosopher of the 20th century.
He was an engineer by education, and his writings deal with mathematical logic, psychology, foundations of mathematics and linguistic philosophy. The whole concept of IQ is controversial (especially when it comes to geniuses long dead), and I have seen estimates of his IQ as being in the range of 190, same as Isaac Newton's.
However, Ludwig Wittgenstein was more than just a great thinker, he was a hero. The man had absolutely no fear. He volunteered to fight in the trenches of world war 1, bullets flew inches away from him more that once, and he was a prisoner of war. Later in life he needed to get had a surgery to remove kidney stones, and he did it ... without any anaesthetics and fully sober.
He was a charismatic teacher at Cambridge, and sometimes he would go silent for minutes in the middle of a lecture (Alain Turing was one of his students, and their arguments about mathematics are fascinating) and no one would dare interrupt him or even make cough / breathing sounds.
His was a badass, and no one talks about the fact that he was actually very funny.
Wittgenstein was without a doubt one of the most fascinating and mysterious geniuses of the 20th century, a man of unparalleled honesty, bravery and eccentricity.
I love Bertrand Russell's quote: "Wittgenstein was the greatest example of a genius as stereotypically thought of: he was profound, passionate, intense and dominating".