A contraction of "All right": a (usually friendly) British informal greeting, not always accompanied by the word "mate". It can be used (and this is not an exhaustive list) on its own, followed by the word "mate", or followed by a name: this latter usage is usually more friendly than the others, as it implies that
you know that person well enough to use their first name in a cheerful and informal greeting.
It can also be used when
questioning the wellbeing of another. However, this will
almost always be preceeded by a word denoting that it is a question, e.g. "you".
N.B. If someone passes you and says "Alright", do not respond "Yes". There are a number of accepted responses, such as a simple "Alright", often followed by the person in question's name, the phrase normally spoken in a more assertive tone, as it is a response, not a question.