Hi Suhaila,
In P6, Budget Expense Cost are usually the Preliminaries cost item in the project such as Project Overheads, Office Hire, Travels, Office cost, safety...etc. You can define your Expenses dictionaries under Admin--> Admin Categories--> Expenses Categories : See example below:

You can enter your budget Expenses on Activity under Details-->Expenses Tab. You can also assign a Cost Account if you are using P6 Cost Account features and defined the cost account categories. On this tab also where you can track/ update and enter actual expenses for each reporting cycle/ cut-off update of your schedule.
Budget Labor Cost is where you enter the all the labor components cost such as Indirect and Direct Cost belong to Project.
Budget Non-Labor Cost is where you enter the all the non-labor components cost such as machine, tools, cranes, loader, franna,...etc, plant & equipment Cost belong to Project.
Budget Materials Cost is where you enter all the materials and major/ minor equipment, instrument purchased for the project.
Depending on the settings, units are may or may not required for entering budget Cost. If you de-link the Unit and Cost (Under Project [window] --> Detail--> Calculations Tab--> Update units when costs change on resouce assignment "not tick" and under Resource Assignment--> Calculate Cost from Units "not tick") then you don't need the labor or non-labor units.