A form of single action mechanism in which the action is cycled by working a lever perpendicular to the barrel of the weapon - in almost all cases the lever swings forwards and down. This was the first repeating action to enter series production and, although long superseded for military use, remains popular with civilians, particularly in the US1.
The lever action is almost exclusive to long arms - mostly rifles and a few shotguns and has served both magazine repeaters such as the family of Winchester Rifles and Shotguns, and single shot rifles such as the Martini-Henry. One lever action machine gun was built - the Colt 1895 - which saw limited adoption and earned the name 'the potato digger' due to its alarming habit of digging a hole with its cycling lever if set up to low to the ground2. This alone should illustrate why violently flailing pieces of metal were unpopular design features for machineguns and why the Colt did not spawn any descendants.
As noted above, the lever action went out of favour with the armed forces of the world - and did so quite rapidly. Despite being ambidextrous and nominally faster to cycle than the systems that replaced it (like bolt action), a lever action has a number of drawbacks, not least that it is nearly impossible to work lying down and that it must be taken out of the aim every shot to be cycled. Also most of the repeaters were built with internal tube magazines, which react badly to pointed ammunition3 and change their balance every time you fire a round.
The other common place to find lever action is in airguns - although here the lever is either used to cock the compression piston or worked repeatedly to charge a compressed air reservoir.