Iyeda:

Dream energy. Aspects of the soul. Big glowing balls of magic. Think of them what you will, they're the things
you're questing to recover in each Nightmare. Comes in five colours:

White: Purity.
Green: Wisdom.
Yellow: Hope.
Blue: Intelligence.
Red: Courage.

Rather worryingly, the first Iyeda you get back in the nightmares is the white one, for purity. Ya don't get Hope
back till the third Mare. So, what, do you just sigh your way through the first two Mares thinking "Oh, this is
pointless..."?

Nightmaren:

The counter to Nightopians (see "Nightopians", unsurprisingly), in that they kill them with extreme predjudice.
They generally are found flying around a lot, getting in your way, firing things at you, and being incredibly 
annoying.

Nightopians:

I'd tell you to "see above", but then there's a very real chance of you kicking me in the shins. Nightopians are 
small, semisentient creatures of Iyeda. They haven't got any knowledge of the human world (we'll ignore the comics
interpretation for now), but they sure have knowledge of humans. Well, actually, that's only a half truth; they have
the knowledge that is possessed by humans. They can see the thoughts of any dreamer that gets into Nightopia 
(christ, I sound like bad fanfiction), and mould the world and themselves around this. For example.. you know the
ones that fish with cake in Splash Garden, right? It's two thoughts, taken together, with no idea of context. The 
Nightopian does as well as it can with the knowledge.

Mepian:

Nightmaren and Nightopians can breed, scarily. Luckily, it's not what you think. If you manage to drill dash a 
'Maren into a 'Pian, their energies merge (jesus, now I REALLY sound like bad fanfiction), and a Mepian is created. 
They appear as a mix of, well, take a guess. The Maren, and the Pian. Apparently, it goes further than that, though.
Mepians can be further mutated by firing more enemies at them, which is nice, I suppose.

Drill Dash:

Press a button. Any button, except the small ones. Congratulations! You've fired off at an appreciable fraction of
the speed of light, and will destroy anything destructable in your path. The drill dash is an absolute necessity for
just about everything in NiGHTS: killing bosses, destroying obstacles (Stick Canyon springs to mind, as does Mystic
Forest), and, naturally, going fast. You try getting above a "B" rank on a level without using drill dash, except
for the boss. It's a hell of a task, let me tell you.

Paraloop:

Fly, fly in a circle. Womph. Now pray that there weren't any Nightopians in that cascading whirlpool of light. The
paraloop is also a necessity for the game, to collect items, kill bosses, and to generally look cool. Any items in
the coruscating swirl immediately think that your pocket is a really great place to spend the day, and any enemies
remain in whatever dimension the paraloop opens up a gateway to.

Items:

Come in various brands. Note that all items are worth double points when you're in Bonus Time, so if you're looking
for a high score, you need to get that Iyeda quickly.

Gold Star: worth 10 points.
Blue Chip: twenty are needed to overload the Iyeda Capture, to get the iyeda within. Worth 10 points, and 50 points,
           redeemable at the end of the 'Mare.  
Gold Chip: once you've overloaded the Capture, all Blue Chips metamorphose into Gold Chips. With Inappropriate
           Capital Letters. Worth ten points.
Bonus Ball: See the number by the ball? You need to get a link equal to that to open up the ball and feast upon
            the point-related goodness within. Worth 1000 points, generally, but I do believe this can vary.
Iyeda Cage: Seven Blue Chips, all for you. Break it with a dash or paraloop, and get yourself a nice little 7-link.
            Worth 280+ points (depends if taken in a Link or not).
That Goddamn Car: If you can steer this thing into its garage on Mare 4 of Mystic Forest, you get a one-time special
                  bonus of 1000 points, and a lovely tinkling sound.
Eggs: Hatches Mepians (if multicoloured) or Nightopians (if dull). Has no real game effect, other than making the
     'Pians happier and thus changing the music, eventually. See "Music" section.