Dimensional analysis is a method employed by scientists to analyse and understand relationships between different properties and quantities of physical things and phenomenons by analysing the dimensions used in their measurement.
Any property or quantity in the physical world is measured in terms of different combination of five basic units. These are - length, mass, time, electric charge and temperature. For any mathematical equation or formula representing a relationship between two or more types of quantities, to be correct, one essential condition is that the dimensions of quantities represented by both sides of the equation should be same.
This fact is used to check the plausibility of equations representing relationships between different quantities and properties. It is also used to identify possible relationship between different quantities, which can be subsequently checked by experimentation or other means.
It is a method used to analyse the relationship between 2 different properties. For example dimensional analysis is used to convert years into seconds or the other way around (this is one of the many examples of what it is used for.)