Latency
In short: The time delay a data packet needs to get from sender to recipient (and possibly back) — usually measured in milliseconds.
In more detail: Low latency is especially important in real-time applications such as online gaming, VoIP or video conferences, where even small delays are noticeably disruptive. Often determined with ping measurements and independent of bandwidth — a line can have a lot of bandwidth and still have high latency (e.g. satellite internet).
In Depth
Latency is made up of several physically unavoidable and technically determined components: propagation delay (the pure time a signal needs to cover the distance — limited by the speed of light, in reality somewhat slower in fibre, about 200,000 km/s), transmission delay (the time needed to “write” a packet onto the line completely in the first place — depending on the bandwidth), and processing/queuing delay (the time every router along the way needs for its forwarding decision and for any waiting in a queue).
Round-trip time (RTT) = outbound latency + return latency + processing time along the way
Propagation delay explains why geographical distance sets the lower limit for latency, no matter how good the rest of the infrastructure is: a connection from Germany to Australia needs a round-trip time of at least around 150-200 ms just because of the distance, even with perfect, congestion-free fibre — no server, however fast, can beat that. Satellite connections (especially geostationary ones) additionally suffer from the enormous detour into space and back, which is why, despite often high bandwidth, they’re unsuitable for latency-critical applications.
Latency is critical to different degrees for different applications: when loading a web page, an additional latency of 50 ms is hardly noticeable, whereas in competitive online gaming or VoIP calls, a latency above 100-150 ms already makes itself felt as a noticeable, disruptive delay.