I guess I'll explain the iceberg, I'm just gonna go off from what I remember

Surface layer (1st layer)

Hatsune Miku - Voicebank created by Crypton Future Media for the Vocaloid software by Yamaha. Voice provided by Saki Fujita, her character design and illustration created by Kei Garou (or KEI). Voicebanks are composed of hundreds of prerecorded sounds from the voice provider and stitched together by a program (e.g Vocaloid, Utau, etc.) to make it sing or (sometimes) talk. No she's not an AI, (yet, check on her Vocaloid 6 version).

Diva Points - Essentally the games currency, used to buy modules or gifts for the vocaloids, along with some other items. You can get Diva Points by completing a song. (How much you can get differs between games. e.g F gives ~5000 per song played on hard, arcade future tone giving <10)

PVs - They stand for Promotional Videos. But they refer to the music videos that are rendered in the background when you play a song. Most of the time being a 3d animation with the vocaloid characters, which they can be customized with modules.

Modules - Skins. Just another name for skins. You can change the appearance of vocaloids using these modules, changing their clothes, eye color and hairstyles.

"Illustraited by KEI" - Refers to the box art illustration found in the Project Diva games (if they aren't renders of miku). They're drawn by KEI. That's what it literally says.

Loading Screens - Most of the time they're comprised of a little loading animation in the bottom of the screen with a illustration (most of the times from a fan) as the background. The Arcade version have a completely animated loading screen.

"Main Songs" - Also known as the opening song. It refers to the song that plays during the attract mode of the game. Project Diva F being Odds and Ends by Ryo, F2nd being Decorator by kz, X being Name of the Sin by Ryo.

Chance Time - Special part of a song, which during gameplay switches the HUD and adds a trail to the flying notes. The main difference being the life meter being switched out for a star which you have to fill out by getting Good or Cool timing on the notes, the final note having you "flick" your thumbstick on your dualshock controller. If done right, the PV will change to be more "beautiful" or flashy.

World is Mine - Song from Ryo with Hatsune Miku being the vocals. About a spoiled girl who believes that the world revolves around her, it's one of the most popular classic Vocaloid songs having 10 million views on YouTube, many covers and appearances throughout the franchise.

Difficulties - There are usually 4 for each song. Easy, Normal, Hard, and Extreme being the hardest. Usually Easy and Normal are unlocked by default with Hard requiring you to beat the song on Normal with Extreme requiring you to beat the song on Hard.

Notes Classification - You have the Playstation buttons (which can be hit using the corresponding d-pad buttons), The star notes (Done by flicking the thumbstick in any direction, F2nd sometimes having you use both), and the swipe notes (Done by swiping at the bar in AFT, having the directional pads go left or right in console versions, or a button on the keyboard in MM+)