We know that he was younger than Aeschylus and Sophocles. We also know that he moved Greek theater in a different direction than the other two. We also know that he won five awards for having the best play of the year, the last one was won posthumously.
The Wikipedia page about Euripides is quite interesting. I especially enjoyed the section on how his plays survived.
Around 200 AD, ten of the plays of Euripides began to be circulated in a select edition, possibly for use in schools, with some commentaries or scholia recorded in the margins. Similar editions had appeared for Aeschylus and Sophocles—the only plays of theirs that survive today: "The rise of Goths and Tartars throughout the Roman world from the gutter to the throne, the destruction of libraries by choleric and fanatical popes and emperors, were unfavourable to the progress but not entirely fatal to the preservation of literary studies." Euripides however was more fortunate than the other tragedians in the survival of a second edition of his work, compiled in alphabetical order as if from a set of his collect works, but without scholia attached. This 'Alphabetical' edition was combined with the 'Select' edition by some unknown Byzantine scholar, bringing together all the nineteen plays that survive today. The 'Select' plays are found in many medieval manuscripts but only two manuscripts preserve the 'Alphabetical' plays—often denoted L and P, after the Laurentian Library at Florence, and the Bibliotheca Palatina in the Vatican, where they are stored. It is believed that P derived its Alphabet plays and some Select plays from copies of an ancestor of L, but the remainder is derived from elsewhere. P contains all the extant plays of Euripides, L is missing The Trojan Women and latter part of The Bacchae.And that's why we have as much Euripides as we do.