The capital structure of a company is the particular combination of debt, equity and other sources of finance that it uses to fund its long term financing.
The key division in capital structure is between debt and equity. The proportion of debt funding is measured by gearing.
This simple division is somewhat complicated by the existence of other types of capital that blur the lines between debt and equity, as they are hybrids of the two. Preference shares are legally shares, but have a fixed return that makes them closer to debt than equity in their economic effect. Convertible debt may be likely to become equity in the future.
Considering the division between debt and equity is sufficient to understand the issues involved.
Simple financial theory models show that capital structure does not affect the total value (debt + equity) of a company. This is not completely true, as more sophisticated models show. It is, nonetheless, an important result, know as capital structure irrelevance.