Both Uses

parliament
in
First Address to Irish Parliament From a British PM
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Today the links between our parliaments are continued by the British-Irish Parliamentary Body, and last month 60 of our MPs set up a new all-party "Irish in Britain Parliamentary Group."†
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parliaments = legislative assemblies that pass laws (existing in some countries)
The Taoiseach has spoken of the exciting new relationships that will unfold as the people of Scotland and Wales, as well as Northern Ireland, express their wishes through their own parliaments and assemblies.†

Definitions:

(1) (parliament with a lowercase "p")
a legislative assembly in certain countries (that can pass laws)
(2) (meaning too rare to warrant focus)
As a proper noun, you need to look at the context to determine the parliament to which Parliament is referring. For example, it could be the British Parliament, the European Union Parliament, the French Parliament, etc.