I hear the word "Gear" often in photography discussion, as in "camera gear". Does gear mean the equipment like the camera itself, lens, grey card? I don't find a definition for it anywhere. Please help me to understand.
gear (noun): supplies, tools, or clothes needed for a special purpose
That's exactly the sense used here. The term includes camera bodies, lenses, tripods, lighting equipment, camera bags, and (although out of fashion now) maybe a vest with a lot of pockets (once common wear for professional photographers).
Note that there is a sense of physicality to the word: one would not normally describe Adobe Lightroom as "gear", even though it or similar software (Darktable, Rawtherapee) is almost essential for modern digital photography. A laptop, though — that could be "gear".
Also, in some parts of the world where British English is dominant (as opposed to American), the word "kit" is used in almost exactly the same sense. In America, the word "kit" in photography means "came in a set with the camera body". This difference occasionally leads to some confusion!
"Gear" is any and all hardware used to produce photographic images.
This includes cameras, lenses, filters, tripods and heads, monopods, bean bags, camera straps/slings/holsters, flashes, light modifiers, reflectors, light stands, backdrops, batteries, bags, backpacks, cases, etc.