You will get to know about it shortly however in short and simple words..
DOM is something like giving each element a name and relation so that we can refer to individual element easily. DOM stands for Document Object Model .. means every element is treated object and part of object and you can easily refer to individual through this model so that in Javascript you can manipulate them as per your need.
On the other hand , Ajax is nothing but Javascript with some small library allows you to make http request without reloading of page.