What is the cell matrix?
The quote (which you more likely got from Wikipedia) discusses multiple types of matrices.

Let's break down the quoted definition: 

The general definition of a matrix would be "an environment or material in which something develops; a surrounding medium or structure." In biology, we think of a matrix as a material, tissue or area in which more specialized structures (molecules, cells, organisms, etc.) are embedded.


In animals or plants, the matrix is often describing a material or tissue.


The nail matrix is the layer of cells that your fingernail or toenail sits on that actually produces the nail. 
The extracellular matrix (or ECM) consists of a collection of extracellular molecules secreted by cells that provides structural and biochemical support to the surrounding [more specialized] cells. One very familiar example of "matrix" tissue is connective tissue. 




Here's a video from Khan  Academy's Youtube channel to walk you through this a bit.  And here's a more graphical walk-through explaining extra-cellular matrices. 

The cytoplasmic matrix (aka cytosol) is the liquid found within cells in which organelles reside. It constitutes most of the intracellular fluid (ICF)


The mitochondrial matrix, a type of cytoplasmic matrix, is the fluid within the inner membrane of a cell's mitochondria that splits it into numerous compartments. This viscous "space" contains the mitochondria's DNA, ribosomes, soluble enzymes, small organic molecules, nucleotide cofactors, and inorganic ions; it is also the site in which oxidation of organic molecules occurs.




So whats this look like under a microscope? Here's an image of a mitochondria and surrounding cellular cytosol under an electron microscope: 


In ecology, a matrix is the general area in which your population, community, or habitat "patch" exists within. In other words, Matrix is the "background ecological system" of a landscape with a high degree of connectivity.