chain conformation
A polymer is a single molecule made of thousands of small units (monomers) linked into one enormously long chain — think of a paperclip chain or a very long string of beads. Now pick that chain up: it can droop into a loose loop, coil into a tangle, or stretch out nearly straight, and it can flip between all of these shapes just by bending. Chain conformation is the word for that shape — the particular arrangement in space a single chain has taken, one of the countless shapes it can flow between without ever breaking a chemical bond.
The key is that the backbone is a string of single bonds (C-C sigma bonds), and a single bond lets the two halves of the molecule rotate relative to each other like a swivel. Each backbone bond can sit at a preferred rotation angle — commonly a straight trans setting or a kinked gauche setting — and choosing trans or gauche at every bond down the chain picks out one overall shape. Because there are two or three choices at each of thousands of bonds, the number of possible conformations is astronomical (of order 3^N for N bonds), and thermal jiggling keeps a chain in a melt or solution constantly hopping between them. This is exactly why conformation must be kept separate from configuration: configuration (the stereochemistry, the cis or trans of a double bond, the tacticity) is fixed by which atoms are bonded to which and can only be changed by breaking and remaking bonds, whereas conformation changes for free, just by rotating single bonds.
Conformation is where a polymer's softness comes from. In a melt or a glass the chains are frozen or wriggling as loose random coils; when you stretch a rubber band you are pulling those coils toward the straight, all-trans shape, and the entropy lost in doing so is the restoring force that snaps it back. When a chain finally crystallizes, it must give up its freedom and adopt one regular repeating conformation (polyethylene lies down in a flat all-trans zigzag; isotactic polypropylene winds into a 3/1 helix). So the same molecule wears different conformations in the melt, the rubber, and the crystal — and which conformations it can reach sets almost everything soft matter does.
Take a single polyethylene chain of 10000 backbone carbons. Let every bond sit in the straight trans position and it lies out as a rigid zigzag rod about 1250 nm long — the shape it takes inside a crystal. Warm it into the melt and thermal energy flips bonds to gauche at random; the chain crumples into a loose random coil only tens of nanometres across. Same atoms, same bonds — just a different conformation.
Conformation is a chain's shape, changed for free by rotating single bonds; configuration is fixed by the bonds themselves.
Do not confuse conformation with configuration. Conformation changes by bond rotation alone (melt, coil, crystal shapes of the same molecule); configuration — tacticity, cis/trans, stereochemistry — is fixed at synthesis and can only change by breaking chemical bonds.