Spychecking is the act of firing your weapon in an attempt to reveal and kill a cloaked Infiltrator. When hit by stray bullets, Infiltrators momentarily drop their cloak, and if the client has particles and gibs turned on, they bleed, making it much easier to hit then with a few follow-up shots; and if they die you will know.
Spychecking shouldn't be confused with pure spam, as checking is generally in sustained bursts in a specific direction while spam is just running around while holding down the left mouse button.
Firebugs are good for Spychecking, as their Flamethrowers set enemy Infiltrator ablaze, marking their location with fire. Afterburn ensures that their locations will be spottable for a short amount of time.