What is the budgeting functions in the business?

It really depends on what type of business you are talking about. In a large corporation, the budgeting functions (or financial analyst, budget analyst function) would be to prepare a yearly budget based on:

1. the previous year's actuals, plus

2. increases to employee hourly wages, and increase/decreases to staffing levels. Increases in taxes.

3. capital projects and other projects.

4. asset management (decrease/increase in depreciation).

5. increase in vendor service contracts.

6. Several other items that may increase/decrease the previous year actuals.

7. It may also be the analyst's responsibility to look for areas to trim the budget actuals from the previous years. Once the yearly budget process is complete, it would be the analysts responsibility to provide monthly variance analysis (actual vs budget) explanations and forecast (budget vs projected) explanations. Not sure why you are asking the question, but if it is that you are looking to take a position like this, you may also be responsible for multiple projects - i.e., process improvement, project management, business planning, trend analysis, etc. Hope I answered your question.