This term is used to refer to other sites that share the same server as you do that use more server resources than they should.
This results in the entire server (and every site on it) running slowly or encountering problems.
Bad neighbors are one reason to avoid cheap shared hosting accounts where one server can host 1000s of websites. They can have a sudden influx of traffic at any given time which can overload the shared server and cause downtime for your site.
The best way to avoid this issue is to avoid using a shared hosting plan and, instead use a dedicated server, which has a lot of other benefits including security and improved speed.