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When participating in internet activities such as games or chat and your internet connection suddenly lags very badly for a brief amount of time. The spike part comes from how sudden the lag is and how high it gets in such a short time.
"I had a huge killing spree going in UT until I got hit with some major lag spike and some fucking noob fragged me."

"Lag spike fucking sucks!"
by IceWarm July 23, 2004