The basic definition of "kensho" is a "seeing into one's true nature." Hakuin, a famous ZM, described all kinds of kensho experiences from small subtle ones to huge mind-boggling cosmic consciousness ones. The main point is that kensho is an EXPERIENCE. Any time the bottom drops out of one's mind, selfhood vanishes, and clarity ensues that's a kensho-type experience. Sooner or later those kinds of experiences come to an end and one returns to ordinary life.
Many Zen people, as noted by Wiki, equate kensho and satori, but I do not. I consider satori something quite different--a realization that ends the spiritual search. That realization is the sudden (timeless) seeing through the illusion of the searcher so completely that it changes one's understanding about what's going on. The search ends because it is seen that the imagined searcher was not the real searcher. The operant searcher is realized to have been Reality, Itself, and the illusion of a "John" or "Jane" having been the searcher collapses. This realization changes everything. Life continues, but there is no longer a person at the center of what appears to be happening. The body/mind, universe, and awareness continue as before, but it is empty of personhood.
After this realization, any previous self-identity like "John" or "Jane" is seen in a new light, as an abstract thought structure that was so ingrained in the organism that is was continually overlooked.
The most interesting question is, "What happens after this realization occurs?" Well, life continues just as before, but without the illusion that there is a separate entity at the center of it. The body/mind goes about its business doing whatever needs to be done, and knows that the real actor is the totality of "what is." The body/mind lives without knowing what will happen next, and is comfortable with that not-knowing way of life.
Zen Masters emphasize the importance of continuing zazen after satori because they think that formal zazen, such as shikan taza, is what led to their freedom from the consensus trance. A few of them seem to realize that it is attentiveness to "what is" that freed them from the mind's domination, but only a few.
Is it necessary to remain attentive after satori? Probably. People who stop being attentive to "what is" often fall back into a mind-centered way of life, and the old sense of selfhood sometimes re-emerges. Gangaji doesn't like the idea of "practice", but she has often said, "Vigilance is necessary." I think what she means by that is what I'm pointing to. Most adults spend 99.9% of their time attending thoughts, and they stay lost in the concensus trance. If one becomes free of the trance, probably some minimal amount of time needs to be spent attending "what is" in order to keep the mind from regaining dominance. FWIW, I've never read anything specific about this issue, so this is just speculation.
When I reflect upon the "Ten Ox-Herding Pictures" of Zen, it seems to me that what I'm calling "satori" is represented by the eighth picture. This means that there are two further stages of development/integration/understanding that Zen Masters point to.