Tier 1 capital is a key measure of capital adequacy. It is essentially shareholders funds including minority interests but with some deductions, divided by risk weighted assets. Preference share capital is generally included, subject to requirements that vary between countries. Preference shares that are cumulative, redeemable, or on which the dividend payments are not discretionary are excluded.
The tier 1 capital ratio is tier 1 capital divided by total assets (including loans to customers). This is a measure of a bank's ability to pay its debts of all types: deposits, bonds, hybrid securities (other than the prefs included above) and any other liabilities under adverse conditions. A bank could lose its tier 1 capital without defaulting on these liabilities, if it lost any more it would default.
The key criteria for the inclusion of prefs is that they are not cumulative or redeemable. In other words hybrid securities are considered sufficiently equity like if there are no payments that have to be made on them, so the bank can skip any payments that it considers it cannot afford (although it cannot pay any dividends to ordinary shareholders either in that case).
Some capital is excluded from tier 1, such as revaluation reserves and intangibles. Some countries allow certain intangibles to be included: most notable large deferred tax assets at major US banks, which lead to the popularity of the previously obscure tangible common equity ratio. This usually means that tier 1 capital is calculated using share capital (including share premium) and accumulated profits: i.e. distributable reserves less intangibles.