Why can a zygote develop into all different types of cell, whereas a differentiated cell cannot? A cell formed by the fertilization between two gametes has all the DNA and can lead the development of a human person (or other animals in other species). But other cells in a human person has also all the DNA (like skin cells), yet they don't lead the development of organs, bones, etc. What is the difference between the zygote and cells from any part of the body from a developed person that one can lead to the development of a person and the others can't in spite of all of them have all the DNA? Does it have to do with the enviroment/surrounding those cells are in, is there any structural difference between the zygote and the other cells or how is it?

Developmental biology is a huge field that we are still working on a lot.

DNA is only half the story. The other half is gene expression; what subset of the DNA a cell is using at any time. Your lung cells have the gene for insulin, but in lung cells, that gene is dormant.

The short answer is that in general, a mature cell is using the subset of its DNA that it needs to do its job and can't just change its gene expression to become a different kind of cell. Cells that do become less like adult cells and less specialized can become cancerous.