So I'm new to this concept and I can't find any proper explanation to this. What does it mean for a reaction to occur in an acidic, basic, or neutral medium?
Description of reactions being conducted in "acidic, basic, or neutral medium" are rather qualitative terms which don't add anything until and unless more details are provided. The first clue is that the concept of pH is dedicated to purely aqueous solutions. All it indicates that an acid or a base was present during the course of a reaction. Neutral usually implies that either the pH was brought close to 7 or no acid or base was intentionally added. pH can be defined for organic solutions but it is more interesting to physical chemists rather than synthetic chemists and it is very hard to quote a pH value when organic solvents are present. For example titration of iron (II) and potassium permanganate is conducted in a highly acidic medium. This is accomplished by adding a small amount of ~ 2 M sulfuric acid. It does not proceed quantitatively in a neutral medium.
Why do we call it an acidic medium instead of acidic solution?
This is just a guess, but redox reactions can take place in solution, on surfaces, in the vapor phase, underground, in pastes found in batteries etc. So to have a single word instead of listing all the different environments, we just say the redox reaction takes place in a "medium" that is acidic, neutral or basic.
There are similar collective terms for other situations in chemistry. If you want to talk about reactants, product, catalysts and spectators at the same time, you can refer to them as "species". If you want to talk about atoms, molecules and ions at the same time, you can refer to them as "particles".