If you are in a pub and someone you are with says 'It's your shout' or 'It's my shout', they mean that it is your turn or their turn to buy a round of drinks.
英英词典释义
Noun
1. encouragement in the form of cheers from spectators;
"it's all over but the shouting"
2. uttering a loud inarticulate cry as of pain or excitement
Adjective
1. noisy with or as if with loud cries and shouts;
"a crying mass of rioters""a howling wind""shouting fans""the yelling fiend"