What is Judo?...
An answer to this question can be can be anything from very simple to progressively complex.
The simple answer is that Judo is the name of a Martial Art and a combat sport discipline that was developed in the late 19th century in Japan from several older forms of Martial Art of jujutsu by prominent Western-leaning Japanese educator Dr. Dsigaro Kano who established Kodokan dojo (that later became Kodokan institute) to develop and promote it. And that this Art still widely practiced today in large number of countries (mainly) as a sport that governed by Kodokan and International Judo Federation (IJF).
The more complex answer will extend this simple definition by adding that Judo still a valuable Art of combat and self-defense and in the course of 20th century it gave start to its - now independent - off-shots as SAMBO and Brazilian Jiu-Jitsu.
I would extend it further by adding that nowadays Judo is a Martial Art that exists in five distinct forms: traditional Kodokan Judo, modern Olympic sport Judo, Kosen Judo, Russian SAMBO, and Brazilian Jiu-Jitsu. (As branching out from Kodokan by SAMBO and Brazilian Jiu-Jitsu, that now having their own governing bodies/federations, doesn't change their nature of been Judo - I'm discussing it on pages for those styles on the site - see Table Of content.)
And this extended answer is just a narrow definition of Judo - Judo with capital "J" (in most of English Martial Art literature its often written in all-low-case - especially in translations of works of Dr. Kano - but on this site I'm using both, capitalized as well as non-capitalized, forms; the differentiation between use of those two forms is also discussed on the relevant pages).