Characters mostly talk. Some can also take real actions that change the game. This page covers which characters can do what.
A character with shop stock can sell to you and buy from you when you agree on a deal. Money and items change hands for real. See Shops and trading.
People taking part in one of your quests (a delivery's sender or recipient, for example) can complete a quest step during the conversation, including handing over or taking the package. See Quests.
Shopkeepers and characters involved in your quests can also:
When a conversation turns violent, the character can take it to the battle screen. Only real physical violence counts, not an argument. Characters set never to fight won't, and you can switch fights off for the whole world with Disable NPC combat in Atlas → Settings. See Combat.
While a character acts, the input says what they're doing. Your wallet, inventory and quest log update as it happens, and anyone called over joins the portraits.
The biggest effects of a conversation happen when it ends: memories, feelings toward you, and notes the character keeps for next time. See Memory and the Journal and Disposition and relationships.