The difference is simply how many separately insulated conductors (cores) the cable carries inside it.
A single-core cable has one conductor inside its insulation. These are the wires you draw through conduit when wiring a building — typically one each for live, neutral and earth — which is why ordinary house wires are single-core. They are easy to route individually and to colour-code.
A multi-core cable bundles two or more insulated cores inside a common outer sheath. This makes a single, tidy cable that is quicker to install and ideal where a complete circuit must run together — appliances, motors, submersible pumps, control panels and flexible connections. APAR's multicore cables come in round and flat constructions (the flat type is popular for submersible pumps).
As a rule of thumb: single-core for fixed building wiring in conduit; multi-core where you want a self-contained, often flexible, ready-to-connect cable. See how to choose the right cable for the wider selection factors.