Move (somebody/something) along something: 1. go along a road, path etc.
"We moved along the motorway until the junction at Swindon."
Move along (usually imperative): 2. to leave and wait in a particular place
The police officer told me: "Just move along, sir."
Something moves along: 3. you are continuing with something and making progress
The work moved along smoothly.
Used in this context, it means can we please speed things up, maybe change the topic?
It implies that the speaker has dwelled too long on one subject, and everyone else is weary of the topic. Particularly if it's in the context of a meeting, and they have a limited amount of time for discussion.