A lag switcher is a person who works the system so that the other players lag while they're connected directly to the host, so they do not. It causes it to be unfair because the people that are lagging can't accurately gauge their shots because the other team or player is spping all around on them, while they're basically sitting ducks.
As far as the internet connection goes, if you have the Verizon DSL and it's anything less then their 3.0M speed, it's not good for gaming as your upload speeds are too low (either 128k or 356k bps) to offer you a good connection.
I would recommend a higher speed connection for gaming, and if Verizon has their FiOS available in your area it really is the best, despite what their competitors claim to the contrary.

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Being loved deeply gives you courage,
loving someone deeply gives you strength - Sun Tzu