The lens diameter HKfan is referring to is the Objective lens, The one at the front of the scope. The other lens, the one you look through is called the ocular lens. Objective lens is the one closest to the OBJECT you wish to shoot. Most scope nomenclature do not indicate the diameter of the ocular lens.
The crosshair(s) are known as RETICLE(s) not Reticule(s).
HKfan is correct regarding his other points. Some others to look at and understand would be:
Exit pupil: The diameter of light exiting the ocular lens and hitting your pupil. Ideally you want nothing less than a 3.5mm exit pupil. The exit pupil is determined by dividing the objective lens diameter by the magnification(max magnification for variables). A 3x9x40 optic would have an exit pupil of 3.6mm which is ideal for maximum brightness at highest power. The greater the magnification/power the larger the objective needs to be to achieve the ideal exit pupil.
Eye relief: The maximum distance your eye can be removed from the ocular lens. For hard hitting or high recoil firearms a greater eye relief is important. Greater eye relief also facilitates a greater range of cheek weld.
Field of View: Distance or area of land visible through the optic at a given range, usually at 100 yards. Binoculars give the FOV for 1000 yards.
Fixed Vs. Variable magnification: Both have good and bad points. Fixed power optics have fewer moving parts and tend to be stronger than variable power scopes. Fixed permits the user to become familiar with one magnification and allows for increased field of view in most cases. Variable permits you to increase or decrease your mag. as required. Variable power scopes can be problematic if the optic has a range finding reticle. Most range finding reticles require you to range at highest power. Often times the user forgets to go to max power before ranging and makes a mistake in ranging. Variables also decrease your field of view at higher magnifications. A smaller FOV makes tracking targets more difficult. For stationary targets it makes little difference. Magnification increases the shooters perceived shakes. Obviously a variable power scope will indicate greater shakes at higher magnification. The great advantage to variables is their ability to magnify to great numbers. This allows the shooter to be more precise in his aiming as well as spot his own hits after the shot.
Most shooters I know use a variable. I use a 2.5x10x42 on my 10/22 for gophers. Most days I never adjust my magnification beyond 3.5. Sometimes I spend hours shooting prone at nothing less than 7x. Its nice to have the option.
Turrets/target turrets: Turrets are the knobs on the top and right side(as seen from behind the rifle) that adjust the reticle and your Point of Impact or POI. Target turrets are usually taller than standard turrets and provide for fast and frequent adjustments. Standard turrets are often protected by caps so that the settings are not bumped or knocked out of place.
Adjustment incriments or clicks: The turrets adjust your POI by a known distance. Most optics are 1/4 inch or 1/4 MOA adjustments. This means for each click of the turret you will move your POI 1/4 or .25 inches at 100 yards. The relationship is linear, the same adjustment while shooting at 200 yards will move your POI 1/2 or 0.5 inches, .75 inches at 300 and 1 inch at 400 etc etc.
MOA is an acronym for Minute of Angle. Which is what your turret adjustments are calibrated for. I've included a link that better describes what MOA is and how it works.
http://riflestocks.tripod.com/moa.html
TDC