The definition
A skills matrix is a grid with people on one axis and skills on the other, where each cell records the level that person holds in that skill. It is sometimes called a competency matrix or a skills map. The point of it is visibility: one artifact that answers who can do what, to what standard, across a team.
Everything useful about it depends on the levels. If a cell holds a tick, the matrix tells you who has been exposed to something. If it holds a level defined in writing — what a person at that rung does differently — the matrix tells you something you can plan against.
Why most of them stop being used
Three reasons, in rough order of frequency. It was built by hand in a spreadsheet, so it was accurate for about a week. It recorded self-ratings, so it measures confidence rather than capability. Or it has no required levels, so every cell is equally interesting and nothing is urgent.
The third is the quietest and the most damaging. A matrix showing that four people are Intermediate at something is a fact. A matrix showing that the role requires Advanced and four people are Intermediate is a decision waiting to be made. Without the required level there is no gap, only a colour.
Building one that survives
Start from a defined taxonomy rather than a list of things the team happens to do — the vocabulary has to mean the same thing to two different managers before any of the cells mean anything. Then set the required level per role before you measure anyone, so nobody is tempted to fit the target to the result.
Fill the cells from verified assessments where the skill matters enough to justify one, and from manager judgement where it does not. Mixing the two is fine as long as the matrix says which is which. A cell that hides how it was filled is the one that gets challenged first.