Well that they were talking about is a general issue you can get if you have a slow internet connection. Even PC games have a hard time connecting to some one over in lets say, Japan or in Europe if you have a horrible internet connection.
The lag you get in the game will differ on how good of an internet connection you have. The Internet is one big computer network so the slower you connection (like dial up) you have, the more latency you'll have between the computers talking with each other. First off you'll have to understand what Lag / Latency is.
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Latency ]
In computing and especially computer networks, a lag is a symptom where result of an action appears later than expected. While different kinds of latency are well defined technical terms, lag is the symptom, not the cause.
Communications latency is the time taken for a packet of data to be sent from one application, travel to, and be received by another application. This includes transit time over the network, and processing time at the source and the destination computers. Specifically, this is the time for encoding the packet for transmission and transmitting it, the time for that serial data to traverse the network equipment between the nodes, and the time to get the data off the circuit. This is also known as "one-way latency". A minimum bound on latency is determined by the distance between communicating devices and the speed at which the signal propagates in the circuits (typically 70-95% of the speed of light). Actual latency is much higher, due to packet processing in networking equipment, and other traffic.
While strictly every packet experiences lag, the term lag is used to refer to delays noticeable to the user. Latency is directly related to the physical distance that data travels. Thus the time taken for a packet to travel from a computer server in Europe to a client in the same region is likely to be shorter than the time to travel from Europe to the Americas or Asia. But protocols and well written code that avoid unnecessary data transmissions are less affected by the latency inherent in a network. Modern corporate networks have devices to cache frequently requested data and accelerate protocols, thus reducing application response time, the cumulative effect of latency. - wiki
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Video Lag ]
You can also experience things like "Video Lag" where your video card can't keep up with what you're doing and your FPS (Frames Per Second) drop. So lets say I'm playing
Warcraft III Frozen Throne at a lan party, and the game is running at a smooth 60 fps (Frames Per Second).
If too many units or animations appear on the screen and my video can't handle it. My fps will drop below 60 frames per second.
People often confuse "Video Lag" with "Internet Lag" because they look the same, and they both result in you getting a delayed result of what happened. Genericnumber1 is welcome to jump in at anytime to correct in typos I may have said
The more you know