Imagine four rods joined together with hinges to form a square. This structure is underconstrained; it can flip about into a rhombus. Now imagine you add an extra rod across the diagonal; the structure is precisely constrained and becomes rigid. It doesn’t matter what length the diagonal rod is (within limits), there will still be a single shape that the structure adopts. Now imagine you add another rod across the other diagonal. This structure is overconstrained; if the extra rod is slightly the wrong length then you will have to force it into position, distorting the structure.

The setup with one diagonal is statically determinate; it has the correct number of links and so cannot have any internal stress without an externally applied load. Importantly, if you apply an external load (for example pulling two opposite corners apart) then you can work out how that load is shared between the links and how much tension or compression each link experiences.

The example with two diagonal links is statically indeterminate, it may have internal stresses, and when an external load is applied you cannot trivially determine how that load is shared by the various links. This was very important when structures were designed by hand; it is much easier to work out how strong each member of a bridge truss needs to be if that truss is statically determinate.

There are mathematical ways of working out if a structure is statically determinate; basically the number of constraints must equal the number of degrees of freedom. But I find it much easier just to consider the intuitive examples.

So does whether a structure is statically determinate or indeterminate mostly serve the analysis stage of construction or do people actually build statically determinate/indeterminate structures and see how things go in order to improve from there?

There are advantages to building statically determinate structures beyond the simplicity of analysis; mostly related to the lack of prestress which means you can get away with larger manufacturing tolerances.

However in practice it is hard to achieve a truly determinate structure, and in many cases it is not necessary to even attempt it. There are analysis techniques that apply to indeterminate structures so it’s not like we just build those blindly and hope for the best.

Thank you kind stranger

You are welcome

People actually build both, but you don't "improve" it from there...you have to decide whether you're building determinate or indeterminate during the design phase. It's going to be part of the design requirements and it's going to influence everything else you do. If you don't know which kind you want before you start, and why, you don't want that person designing structures.