Delay is the time it takes for a packet to go from the source to the destination. Packet delays are typically measured in thousandths of a second or milliseconds (ms). If you think of a highway between two cities, regardless of the number of lanes (the bandwidth), the time it takes for a car to travel between them is the delay.
More specifically, large changes in delay (a high delay variation) can be especially problematic for interactive applications such as VoIP and video conferencing. Online gaming can also be impacted if the delay variation is high enough.