When an airplane needs to taxi into a runway, clearance from air traffic control (ATC) is required.
Before giving out clearance to enter the runway for takeoff or wait, ATC will instruct the airplane to "hold short" at the runway to avoid incident, which is a line that all planes must stop. The line is drawn on the taxiway with 2 solid and 2 strip lines, with blinking yellow lights on the taxiway. It is also identified by a yellow sign for that intersection and a red sign for the runway identification.
When a plane goes beyond that line without clearance, it is basically means that the pilot disobey the ATC instruction. Although it is a serious issue, it does not necessary cause problems.