Latency, often called ping or maybe delay, is the total time it takes for a message to go from your computer to a server and back to your computer. Technically, latency should exclude the server's processing time, but this should be very minimal. It's basically how responsive things are. Latency is unimportant for some things like video streaming or downloading large files, but it is key for things that require instant responses, like gaming. It also makes general web browsing more responsive.
Latency is usually measured in milliseconds, one-thousandths of a second. A ping of 100ms means that it takes one hundred one-thousandths (one tenth) of a second for the packet to make a round-trip.
High latency is often caused by the same things as packet loss, but it can never be completely eliminated. The absolute physical minimum latency is based on the speed of light. Keep in mind the physical distance between you and the server you are connecting to. For reference, one light-millisecond is roughly 186 miles or very close to 300 kilometers. (It takes light 1ms to travel ~186 miles.) Given that most communication happens at well under the speed of light, distance can quickly become an issue for faraway users. This is also one of the biggest drawbacks of satellite Internet, as you literally have to shoot the packets to space and back before they can start their journeys through the cables.