A maturity grid, also called a maturity model, is an assessment tool for evaluating an organization's level of progress towards a goal.
The grid, which is a matrix laid out in rows and columns, typically lists the criteria that will be evaluated in the left-hand column. Each column's corresponding row has cells that describe, in a few words, the typical behavior exhibited by an organization at each level of development. Typically a maturity model has ten rows or less, with the first row defining entry level and the last row defining fully-developed best practice.
Maturity grids can be used to provide an organization with an initial benchmark for how close to 'fully developed' an organization is in regards to the criteria being assessed. They are also useful tools for leading discussions and providing management with roadmap for next steps.
This video from the UpTime Institute explains The Green Grid is using a maturity model to inspire data center administrators and vendors.