Maybe visually would help. Definitions usually have a lot of mathematical jargon.
In: Mathematics
A quantile is like a bin. Think of it like sorting gravel. You have a big conveyor belt carrying rocks that you want to sort. You set up a vibrating mesh tray with specifically sized holes in the mesh to let tiny rocks through (say, less than 1 mm in diameter). It vibrates to jostle the rocks and keep things moving along. The next mesh has 2 mm holes in it, to catch small rocks. The next is maybe 5 mm, then 10 mm, then the rest is waste (too big for gravel).
What you’ve done is binned your gravel by size. The first quantile is smallest (<1 mm), the next is larger (1-2 mm), the next larger (2-5 mm), and the last is largest (5-10mm). It’s just a way of expressing sorting into groupings.
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