what are financial projections?

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Financial Projections are basically Forecasts of financial figures or data. You project the actual or budgeted data/figures into the future to get an idea of what things will be like if you pursue a particular decision or a course of actions. Financial Projections always have a set of assumptions on which they are calculated.

For example you want to Project what ice-cream sales will be like during summer months. You can either use actual data or budgeted data and apply your assumptions on that data like for instance 'according to weather office there will be a sharp rise in temperatures in Delhi and also an increase in foreign visitors due to which ice-cream sales will rise by 80% as compared to same month in last year or as compared to last quarter ice-cream sales'.
So using this and other assumptions you project Sales Revenue figure in INRs as well as quantity.

Hope that explains your question. If not do let me know.