It may have equal or nearly equal power with the lower house.
It may have specific powers not granted to the lower house. For example:
It may give advice and consent to some executive decisions (e.g. appointments of cabinet ministers, judges or ambassadors).
It may have the sole power to try (but not necessarily initiate) impeachment cases against officials of the executive or even judicial branch, following enabling resolutions passed by the lower house.
It may have the sole power to ratify treaties.
In some countries, its members are not popularly elected; membership may be indirect, hereditary, ex officio or by appointment.
Its members may be elected with a different voting system than that used to elect the lower house (for example, upper houses in Australia and its states are usually elected by proportional representation, whereas lower houses are not).
Less populated states, provinces, or administrative divisions may be better represented in the upper house than in the lower house; representation is not always intended to be proportional to population.
Members' terms may be longer than in the lower house and may be for life.
Members may be elected in portions, for staggered terms, rather than all at one time.
In some countries, the upper house cannot be dissolved at all, or can be dissolved only in more limited circumstances than the lower house.