The Mars table is a five by five square of the numbers one to twenty five, adding to sixty five in every row, column and diagonal, and to three hundred and twenty five in total. Odd ordered squares like this one and Saturn's are the easy cases: a straightforward construction rule, known in several traditions independently, fills them without trial and error, which is part of why the odd planets' tables are the most stable across manuscripts.
The names attached to it follow the same derivation as the rest of the set. In Agrippa's scheme the intelligence of Mars is Graphiel and the spirit Barzabel, each built so that the numerical values of its Hebrew letters return a number from the square. A reader who wants to check the system rather than take it on trust can do so here with a pencil.
The wider point about the Mars table is what planetary magic thought it was doing with any of this. The squares were not decoration and not, in the intention of the writers, symbols. They were held to be the mathematical form of a planetary influence, so that engraving one on the correct metal at the correct hour produced a physical object in which that form was present. The atlas records the practice as documented rather than effective, and records the arithmetic because the arithmetic is real and checkable even where the claim built on it is not.
Agrippa published the tables in 1533. The manuscript tradition behind them is older and Arabic in large part.