Why do we use WACC for DCF?

Don't feel like an idiot! Everyone starts somewhere.

When you perform a DCF analysis, most of the time it is based on discounting free cash flow to the firm. Since this type of cash flow is attributable to both debt and equity holders, you have to discount it by a rate that appropriately represents a mix of costs of debt and equity, which is your WACC.

Costs of capital reflect the amount of risk both equity and debt financers take on. If you are a highly leveraged firm, or you operate in a risky industry, it's likely the debt you take on would be at a higher interest rate and your equity holders would demand a higher return. Hence, the WACC represents your costs of debt and equity capital that's weighted by the proportions on your capital structure.

Hope this makes it clearer.