Fuller
From SwordWiki
The "fuller" is a groove or indentation on the flat sides of the blade, either beveled or rounded, that is designed to reduce weight and improve handling by controlling weight distribution, and in some cases enhance the flex of the blade. Some fullers are very wide, and others are narrow grooves, of which there may be several on a single blade.
The fuller is NOT a "blood groove" as you may have been lead to believe. The concept of a "blood groove" is one of many nineteenth century myths perpetrated by scholars and authors of that century. There has been speculation that the groove might make it easier to withdraw the blade from the target, but no known direct evidence exists that it in some way reduces hydraulic resistance. It could be argued that the increased surface area may actually have the opposite effect.
