Multi-turn dialogue is a conversation that does not end after one question and one answer, where both sides exchange several messages in sequence. The hard part is that the system has to read each new message in the light of the turns before it. "What about shipping" means nothing on its own and only makes sense if you know which product the previous turn was about.
On the model side this is handled by putting the earlier turns back into context. The whole run of user and assistant messages is resent with every request, because the model keeps no memory between calls. As the conversation grows that accumulation fills the context window, so applications move to summarising older turns or retrieving only the relevant parts.
A dialogue system has other problems to settle too. What a pronoun refers to, the moment the user changes subject, cancelling an earlier request, and asking a question when information is missing all belong to this layer.
A worked example: a travel assistant is asked for "Monday flights to Izmir", then "show me the morning ones", then "actually check Tuesday as well". By the third message the origin, destination and morning filter still apply and only the date has changed. If the system cannot carry those forward, the user has to restate everything each time.
Instruction drift is common in long threads. A rule set at the start can lose its grip twenty turns later, which is why critical constraints get restated on every request.