We can only speculate, since the text doesn't explain.
1. We know that there are several themes to the Thessalonian books: (1) God is going to bring creation to its intended destiny; (2) God is working for the salvation of humankind; and (3) there was great confusion about Jesus's second coming that had to be straightened out.
2. We know that Paul's visit to Thessalonica (Acts 17.1-9) was met with persecution and rejection based on false accusations and misinformation.
3. We know that one reaction to the idea that Jesus was coming back soon was to quit work and idly wait. This was a perspective and lifestyle that Paul argued against.
So it's not too tough to piece together a plausible picture. These "busybodies" weren't lazy, they were working towards the wrong end, persuading people in the wrong direction, and irresponsibly sponging off the community. They were working towards the wrong end because they were probably trying to convert people to their way of thinking and way of life instead of trying to convert the lost to faith in Jesus. They were persuading people in the wrong direction because they were probably convincing others to quit their jobs as well. They were sponging off the community, taking money from hardworking people instead of getting a job themselves. It's not that they were lazy, but probably rather they were not working because of their theological position—too pious to work. "Hosh posh," Paul was saying. "Get a job (v. 12), and do the work of ministry, not of misdirection."
As busybodies, they, because of their abundance of leisure time, were poking their noses in where they didn't belong, theological snobs, and they were influencing others. Paul's done with that (vv. 6-10).