Definitions
Capital
A different word for money. Everyone wants this. Comes in various different forms: stocks, physical dollar bills, a bank account full of money, but always comes down to something valuable to someone.
In relation to a company, capital often refers to the money it has to use in order to make more money. Companies often sell stocks and bonds to get capital (i.e. money) which they can use to buy equipment, buy land, pay for marketing, hire more staff, etc.
Weighted Average Cost of Capital
Capital (money) is used by a company to make more money. Often capital comes from selling stocks & bonds. Each has a cost associated with getting it, i.e. the Cost of Capital. For bonds this is its periodic interest payment. For stocks it can be dividends it must pay or the rate of growth (& thus price increase in stock) the company must achieve.
Weighted Average means that the proportion of each, bonds or stocks, is taken into account when calculating the “cost of capital”. If a company has 60% bonds and 40% stocks, the cost of capital should be bond interest rate x 60% + (stock price growth rate x 40%), thus giving each type of capital its own weight.
More on Weighted Average Cost of Capital at Wikipedia
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