Message pausing can be done from Messaging UI for any messages that are mid-send (i.e. the message status is 'Active').
This might be because, for example, a typo has been spotted in the message content, because an incorrect link has been included, or because the message targeting or time window needs amending. Or simply because you want to stop any further recipients getting the messages (in this respect pausing a message can be thought of as stopping a message, although with the opportunity to re-start sending if the time window allows.
Typically this will be for a triggered message, i.e. one with a time window during which time it is active) because a broadcast message by definition is only 'active' for a very short period of time (namely the time at which the message is set to broadcast).
Note that pausing a message is designed for a short pause period. App users who qualified during the time the message is paused WILL be sent the message once the message is unpaused. If a long time elapses between pause and unpause, then the message might be received out of context with the action that triggered it originally (e.g. entry or exit from a region).