Light from an ordinary source vibrates in every plane at right angles to its path. Plane-polarised light vibrates in only one plane. A polariser (such as Polaroid) transmits one plane and absorbs the rest.
A substance is optically active if it rotates the plane of polarisation. This happens when its molecules are chiral (non-superimposable on their mirror image), e.g. a single enantiomer of a compound with a chiral carbon.
One enantiomer rotates the plane clockwise (dextrorotatory, +); its mirror image rotates it equally anticlockwise (laevorotatory, −). A 50:50 racemic mixture gives no net rotation.
The analyser is a second polariser, rotated until the light passes through brightest. The angle it must be turned through is the observed rotation, which depends on the substance, concentration and path length.