A reconstruction of a solve is an annotation of the exact moves performed by a cuber did during a solve. Reconstructions are commonly broken apart into the sub steps used by the cuber.
Some cubers known for doing many reconstructions are Lucas Garron, Michael Gottlieb, and Rob Stuart.
A reconstruction of one of Feliks Zemdegs's 3x3x3 World Record solves by Michael Gottlieb:
scramble: L2 R2 F R2 B2 L2 D2 F' D' L' F' U2 B U2 L F2 D' B L2
inspection: z' y
cross: r' D R U' D2 R D'
F2L1: U L U' L'
F2L2: U y' R U R'
F2L3: U' R' U' R U' R' U R
F2L4: y U' R' U R U R' U' R
OLL: U U2' R' F R U R' U' F' U R