In a laymens term summary, a stress path will tell you if the soil is over under consolidated (uncommon, unloading stress condition), normally consolidated (never been consolidated more then that), or over consolidated (was once more heavily loaded, was compressed more then it is now and has since "unconsolidated").
In terms of geological history, an normally consolidated soil would be once that has not been stressed more then it has been now. A residual soil, formed from bedrock weathering, a soil placed from water deposits, etc, could be normally consolidated. An over consolidated soil could be a soil that was placed and then had the overlying soils eroded away, or could have been under a glacier and the glacier traveled over it and melted away, for two examples.