An Arc-Fault Circuit Interrupter (AFCI) or Arc-Fault Detection Device (AFDD) is a circuit or equipment protective device designed to prevent fires caused by electrical arcing.
AFDDs included in equipment will often use optical or RF sensing sensing to detect an arc. Devices intended for complete circuit protection will usually detect the characteristic current profile caused by electric arcing, and disconnect the affected circuit.
Ideally they will detect line to earth as well as line to neutral (i.e. in circuit) arcs. (Note that a RCD will normally detect Line to earth current flow, but not L-N arc currents, since these don't usually cause a current imbalance).
AFDDs are popular in some countries (notably the US), but have not so far been commonly found in domestic situations in the UK. However the 18th edition of the UK Wiring Regulations does now include provision for inclusion of AFDD protection at both the equipment level and at the origin of a circuit in a consumer unit (See reg 532.6 for details). Note the 18th edition does not prescribe or mandate their use, and so it would fall to the system designer to specify them if required.
 Domestic fires caused by arc faults are far more common in the US due to the use of lower voltage supplies (hence higher circuit currents), use of aluminium cables, and also the relatively poor quality of some of their wiring accessories).