Linear referencing is used to define features in relation to existing line features. These new features can either be points or lines. For example a water monitoring station can be defined as 300m along a section of river, or a stretch of road can be defined as requiring repairs, from 220m along to 270m along. Most GISs implement this functionality – for details look at the ESRI and GRASS help pages.
In terms of storing linear referenced point features, you only need three fields – an ID of the original line feature, an ID of the feature to reference along the line, and a M value – the measurement along the original feature. Line features require two measurement fields, a starting distance, and an end distance.
