Action (Fishing Rod): This has to do with the amount of flex in the rod and the way the rod curves when under load, i.e. fighting fish or casting.
Defining rod action tends to get a bit confusing but in Australia I believe it can simply be applied to the type of game you're chasing. For example, big, hard fighting fish that need strong line and heavy lures will need a Heavy to Extra Heavy Action Rod. The opposite can apply to light action rods. Medium action rods lay in the middle and are the most common action fishing rod. 

Action (Fishing Lure): How the lure moves through the water. 

Bait: This can be a general term to describe any natural or man made item used to attract fish. Or it can be applied specifically to natural food items that a fish would eat.

Barb (Hook): Is a angular piece that juts out from a hook just below the point to make it harder for a fish to dislodge the hook once the hook has been set.

Barbless (Hook): Does not have a "barb" to enable an easier removal of a hook, and less damage to fish.

Burn and Kill: This is a term used to describe a method of lure retrieval where you quickly retrieve the "bait" and then stop suddenly to let it pause in the water. 

Butt (Fishing Rod): This is the base or handle of the fishing rod 

Fighting or Playing fish: The contest between man and fish, when a fish has been hooked and the angler is trying to get it out of the water.

Jigging: Is a method of using a "bait" in a vertical up and down motion by lifting and lowering the fishing rod to entice a fish to "strike".

Leader or Trace: These include fluorocarbon, monofilament and wire. They are the last length of line that connects to your hook, lure, fly etc.

Main Line: The is the bulk of fishing line that is wrapped around a fishing reel and provides the primary connection from reel to rig.

Memory: Sounds silly but what “memory” refers to is the lines ability to maintain a shape. Fishing line is usually wound around something round like a spool. You have probably noticed that monofilament line will have bends in it when relaxed. This is because it has “memory” of what it has been doing most of the time, which is wound in a circle around a spool. No memory allows better casting.

Pelagic: Refers to fish who inhabit the open oceans and who are generally found in the middle or upper water column.

Rig: Is a collection of "terminal tackle" used together in an arrangement to target a fish species. Generally it will include at least 2, possibly all, of the following; line, hook/s, swivel/s, sinker and float.

Running Sinker: This is a "sinker" that is unrestricted and free to move up and down the main line.

Setting the hook: Is about increasing tension on the fishing line to embed the hook in a fishes mouth when you feel the fish has engaged the "bait". 

Sinker: Is a weight used to sink line and bait in the water.

Snag: Not a sausage or sensitive new age guy, but basically a "structure" that you have or could potentially hook on to.

Snap: Is a piece of equipment that is commonly used to attach fishing line to lures and enable quick lure changes.

Swivel: Is a piece of equipment that attaches two lines together and spins independently so that the line doesn't twist. 

Strike (Angler): This refers to "setting the hook" by pulling the fishing rod away from the fish (towards yourself) to tighten the line and hook the fish.

Strike (Fish): Refers to a fish attacking the "bait".

Structure: Is the physical formation of an object/s or landscape in relation to fish habitat, either underwater, on or just above the waters surface. These can be natural or man made for example, trees, rocks, pylons, jetties, bridges, FADs, bomboras, reefs, rock shelfs, islands, mangroves, steep drop offs, breakwalls, reeds, even weed beds can fall under the "Structure" definition when fishing.    

Taper (Fishing Rod): Rod taper refers to the way the rod narrows from butt to tip. This effects the action of a fishing rod. A rod that flexes mostly at the tip has a fast taper and a rod that flexes through it's entire length has a slow taper. Generally speaking fast taper is better for lure fishing and slow taper is better for bait fishing. 

Terminal Tackle: This is a term used to describe any gear that is used at or near the end of a fishing line (the “fishy” end). Hooks, Sinkers, Jig Heads, Swivels, Snaps, Floats, Lures etc all fall into this category.

Trolling: It the process of dragging a type of "bait" behind a watercraft to catch fish. 

Walk the Dog: Is used to describe a style of action that surface lures like pencils or stickbaits impart when being retrieved in combination with a special rod technique.