Bend a paperclip a few degrees and let go, and it snaps straight back to its original shape as if nothing happened. Bend it much further and let go, and it stays bent — the metal has taken on a new permanent shape, and no amount of letting go will undo that. Both bends are the same wire, the same metal, the same force applied the same way. What changed is how far past a specific, measurable threshold you pushed it, and that threshold is one of the first things a structural or mechanical engineer has to know about any material before they're allowed to build anything out of it.
Two very different kinds of bending, back to back
Load a material gently and it deforms elastically: stretch it, bend it, compress it, and the moment the load comes off, it returns to its original shape, with the amount of deformation rising in direct, predictable proportion to the load the whole way — that proportionality is Hooke's law, and it's what a "stress-strain curve" looks like as a straight line for the first part of the graph. Keep increasing the load past a point specific to that material — its yield point — and the material stops returning to its original shape once the load is removed. It's now deforming plastically: the internal structure of the material has permanently rearranged, and letting go only recovers the small elastic portion of the bend, leaving the rest as a new, permanent shape. The paperclip that springs back and the paperclip that stays bent are two different regions of the exact same curve, and the yield point is the border between them.
Why "just below the border" is the whole design job
Nobody wants a bridge, an aircraft wing, or a bicycle frame to permanently deform under its normal working load — that would mean every load cycle leaves the structure a little more bent than before, which is a slow-motion failure in progress. So engineering practice keeps the working stress a material will actually experience well below its yield point, with a deliberate safety margin, precisely so the structure stays in the elastic region for its entire working life and returns to shape after every load, indefinitely. Knowing where the yield point sits for a given material — and how that point shifts with temperature, with repeated loading, with the exact alloy or treatment used — is a large fraction of what a materials science and structural design curriculum is actually teaching underneath the maths.
What we're still unsure about
This elastic-then-plastic story describes ductile materials — most metals, most plastics — well, but it doesn't describe every material's behaviour. Brittle materials like glass, ceramics, and some cast irons have little to no plastic region at all: they deform elastically almost all the way to failure, then fracture suddenly, with no bent-but-not-broken middle stage to observe on the way there. Treating "bend a little, then bend a lot, then it breaks" as a universal description of how solids fail would be quietly generalising from ductile metals to a much larger category of materials that don't actually behave that way.
This sits inside Strength of Materials & Stress-Strain Relationships, one of eight topics in Mechanical Engineering, one of four domains in Engineering, one of seventeen subjects the app can quiz you on.