It varies!
Grassblades started as a "I want to do a story about a grumpy guy travelling with a little girl, because that's fun!" and then kinda... grew into a sprawling epic. Character-designs, plot-ideas, outlines, scripts, etc., kinda came together slowly, in bits and pieces, over a period of several years.
With Stranger Things, I came up with the plot first, and then designed characters to fit it.
Some of my ideas grow from characters I've doodled in my sketchbook and enjoyed. Others start as brief central ideas - like 'a winter fairytale set in a desert', or 'a world where the lights have gone out' or something - and then grow from there.
You should have character-designs and a script/outline down before you start drawing the actual finished pages, but there are no rules for where you start planning.