Translation moves an object from one position to another in 3D space by adding a translation vector (Tx, Ty, Tz) to the original coordinates (Xold, Yold, Zold). The new coordinates (Xnew, Ynew, Znew) are calculated by adding the corresponding component of the translation vector to each original coordinate. Translation can also be represented using matrix multiplication, where a translation matrix T is multiplied by the original position vector P to yield the new position P'.