Breaking is a term used in war between alliances on alliance-based servers, when countries repeatedly attack another country to reduce its defences so that other countries with lower networth may attack it until it is dead.
During a kill run, an amount of military units, such as troops or jets, to send at a target is referred to as the break (i.e., break their defenses). The break is more often than not set to enable successful attacks against the target. However, in some cases, such as when lemming is needed to bring a target down to where it can then be broken, a break may be set for the sole purpose of killing a target's defensive units, regardless of whether or not the attacks are successful.
Break also refers to the act of killing a target's defensive units so that countries with less offensive capabilities can successfully attack the target. Countries who do this are referred to as 'breakers'. Countries who participate in the same kill run and immediately benefit from this are referred to as 'mid-breakers'. Mid-breakers are usually noticed by their networth and/or military makeup. After the mid-breakers have brought the break down some more, countries referred to as 'finishers' may take over. 'Finishers' are aptly-named, for they're usually the countries known to be finishing a kill run on a target, by sending the last attacks. Finishers are usually the smallest countries available during a kill-run. Most restarts will be known as 'finishers' until they start breaking enemy countries for others to finish.