In ordinary talk, a sector is one flight.
To be more precise a sector is the time defined as "from when an aircraft first moves under its own power to when it comes to rest (hopefully) on stand".
In terms of flight duty - you can normally only do so many sectors in so many hours. Every country is different, but for example UK rules you need to know (inter alia) what time they reported, and how many sectors. A table then tells you how long they can operate.
Please do not ask for any further details on how flight duty is worked out, as it can be extremely boring!!
all the best
c