Attributes in Diablo 3 consist of Strength, Dexterity, Vitality, Willpower. Each attribute affects multiple values in Diablo III; making points in each attribute valuable to all characters. See the respective character class page for Barbarian, Witch Doctor, Wizard, monk, and the Upcoming Classes for more specific details.
Leveling is a way of indication that your character is developing, usually by killing monsters and gain experiences. New Levels access to new features such as new abilities, spells, talents and items. Currently the plan is there will be 100 levels in Diablo 3, which will take a while to reach.
Strength governs how much damage you do and how high your armor rating is. Whether the effect of each point in Strength on the secondary attributes is the same for every character class is unclear as of yet.
1 point of Strength gives:
Dexterity governs your chance to critically strike a target, and so doing more damage. Dexterity influences your chance to dodge an attack and lowers the chance that your character will be interrupted by getting hit.
1 point of Dexterity gives:
Vitality governs the amount of life your character has and how fast its mana regenerates.
1 point of Vitality gives:
Willpower governs the amount of spell damage bonus and extra health the consumption that a health globe will grant your character.
1 point of Willpower gives:
Critical hits are special types of hits dealt to monsters (and other players in PVP). Critical hits can happen from any type of damage (weapon or spell), they deal bonus damage, and may trigger other special effects as well. Monsters that die from critical hits usually explode in an especially gruesome death animation, adding visual fun to the killing bonuses.
Exactly how critical hits work and how much damage they deal isn't yet entirely understood. This is partially due to the fact that the game remains under development and that the features are in flux, but it's also due to critical hits doing a lot of different things in Diablo 3. In previous games in the series critical hits were simple; they doubled physical damage. In D3, the biggest change is that critical hits work on all types of damage. Not just physical, or melee, but various types of spell damage as well, and apparently they can trigger from elemental damage on weapons as well.
The basic critical hit bonus is still +100% damage, but various skills increase the damage of critical hits, while others increase the odds of critical hits scoring, or cause other effects to trigger when a critical hit is scored. How these will all interact remains to be seen.
The calculation of the bonuses is going to be interesting as well. In D1 and D2, critical hits were a huge bonus, since doubled the total physical damage dealt; a value that was often in the 1000s for a powerful combat character. In D3 critical hits will still (apparently) be that powerful for the Barbarian, but critical hits on spell damage would seem to be far less potent, since spells generally deal their damage over time, rather than in huge chunks per hit. Occasionally adding 10% to the critical hit damage of a 1-6 damage spell isn't very impressive, even if the spell is hitting 20x a second. A wizard would seem better off boosting the % chance of scoring a critical hit.
Monsters that die to a critical hit get a special "critical death" animation, which is extra gory. A few examples can be seen in screenshots on this page. The monsters literally explode, leaving chunks of themselves scattered across the ground. These animations are customized for whatever type of damage killed them; the chunks have flames licking across them from fire damage, sparks and arcs from lightning, etc. Physical damage critical deaths tend to leave huge slicks of blood, and give a battlefield a lovely post-massacre patina.
Critical hits are a major part of the game in Diablo III, dealing double damage with every type of damage, inflicting bonus effects, boosting and being boosted by a wide variety of skills, and triggering special (extra gruesome) death animations.
This is a partial list, since the game is still under development and skill descriptions and functions are bound to evolve over time. Looking at what sorts of skills add or otherwise interact with critical hits can be illustrative, though.

The Barbarian has a number of skills that increase the % damage of his critical hit, and a few interesting skills that boost other properties (such as fury generation rate and defense) when he scores critical hits. There aren't any known skills (yet) that increase his chances to score critical hits, though.
No critical hit bonuses from Witch Doctor skills are yet known. This isn't a sign that there aren't any, though. It's just due to the WD only having 11 skills on display at BlizzCon 2008, while the Wizard and Barbarian had more than 50 each.

Most Wizard skills seen at BlizzCon 2008 displayed the bonus provided by a critical hit of that type of damage (cold, lightning, etc), but there were fewer skills that actually boosted or affected the frequency of his critical hits.
No skills in this tree listed bonuses related to critical hits as of October 2008.
No skills in this tree listed bonuses related to critical hits as of October 2008.
Health Globes are orbs of life energy that can escape from killing monsters. There are also Mana Globes.
Drop Rates: 25%-30%
Boss Battles: During Boss Battles, where no extra monsters are killed, individual hits on a boss will have a (low) chance of spawning a Health Orb.
These globes of health work as you would expect, when stepping on them, you will get an increase in health. The increase is over time, so not instant, and you only activate them if you are lacking health. The interesting thing about multiplayer and orbs is that they heal all party members in the vicinity, enabling any player to be a makeshift healer. Even if the person picking the orb up is at full health, it will heal others.The drop rate is quite low, but with the amount of monsters coming at players, there should rarely be a lack of orbs, and when they are far between, there is always potions. Additional tweaks have also been promised.
Source
Health orbs heal on a % basis; if they fill say, 25% of a character's hit points, then a Barbarian would get more actual health from one than a Witch Doctor, even though both would see their health globe fill the same amount.
Mana Globes are orbs of magical energy that function much like health globes; they restore mana (25% of the maximum was the listed amount) when a character runs through them. As you might expect, they look just like health globes, but are blue, instead of red.
No mana globes were seen during the BlizzCon 2008 demo play, and they are only mentioned in the description of the Mana Recovery spell. The only thing we know for sure is that they drop for Wizards, with skills in Mana Recovery. It's not known if they ever drop when a Wizard with points in that skill isn't around.
From one perspective it seems likely that Mana Globes only drop when a Wizard is around, and considering the loot system it would only be visible for the Wizard. Health Globes work completely opposite of that, dropping for all players and usable by all, healing all in the vicinity. It's also possible that the Mana Globe functionality is similar to that of the Health Globe.