"Combo skills" or "combos" were a term Blizzard used during development to designate the melee-hitting, Spirit building Monk skills. There were initially 7 combo skills, but the term was phased out during development, and the skills were tweaked as well.
In the final game these skills are all found in the Primary skill grouping, and there are only four of them that build Spirit with each hit on a valid target: Fists of Thunder, Deadly Reach, Crippling Wave, and Way of the Hundred Fists.
Earlier in development Dashing Strike, Exploding Palm, and Sweeping Wind were also combo skills, though none of these work in that fashion in the final game.
Combo Skill Function
Early "blood supernova" version of Exploding Palm's 3rd hit.
Though no longer called "combo skills" these skills are powerful attacks and amongst the Monk's best forms of damage output.
All such skills have three stages that work in rapid succession, with each of the three attacks dealing some special effect, and a special bigger effect on the third hit. There is no UI component to visually signify which level of charge a Monk is using, though the first and second levels have distinct graphics, and the third is always a huge explosion or other visually-distinctive effect.
Combos always count up to three and then reset; it's not possible to build up multiple combos to the second or third level at once, as the Assassin could do with her charge up attacks in Diablo 2. Monks can mix and match their combos; the three stages can come from two or three different combo skills, but they always proceed in order, with the first, second, and third stages in sequence, regardless of which combo skills are used.
While there was much speculation about mixing and matching combo sequences pre-game, in practice in the final game most characters use just one combo at a time, or else use two to gain some buff or deal a debuff with one of them. Hardly anyone bothers to mix and match within the same three-hit-sequence, though. The game is too fast-paced to be that specific and technical in practice.
Combo Visual Indicators
Combos go very quickly, with the three hits in a bang-bang-bang sequence by a Monk hitting at 1.5-2.5 attacks per second. Each of the hits is also delivered with a unique animation, as you can see in the sequence of shots showing off Hands of Lightning below. That's a good thing, since the developers have not included any UI mechanism (like the swirls of light the Assassin got with her charge-up skills in D2X) to visually-indicate the combo level.
We don’t want tracking of combo stages to be so important that there needs to be a UI element to keep track. It should be that if you’re up on your game you’re tracking combo stages and it helps you get a slight edge, but if not you’re kicking ass anyway and will probably do fine.
Hands of Lightning
combo sequence showing off the three hits and their varying animations.
The functions of different moves from the first, second, and third level of a combo skill were simplified during development, as Bashiok explained in an April 2011 forum post:
Will the UI allow for keeping track of which combo you’re on? His combo skills are really exciting but I’m worried it’ll become too much of a chore playing the entire game counting out my attacks in sequences of 3. It would be unfortunate to unleash a 2nd tier hundred hand attack at range expecting to dash forward because you miscounted.
Bashiok: ...we have made changes to skills so they’re consistent; such as making all stages capable of a dash. We don’t want the situation you’ve described to be an issue.
I think what Bashiok means is that if the first part of 100Fists was a dash, then the second and third parts would also include a dash.
Bashiok: Right. The final stage on combo skills is still usually the powerful topper. I was specifically referring to a movement component not being tied to a specific stage of a combo skill (if it exists). There is some spreading out of mechanics to ensure really important pieces like movement and damage mitigation can’t be ‘missed’ because you counted wrong. But doing damage is doing damage, for the most part, so big combo finishers still very much exist on the third stage.
Early Monk Spirit Generators
Spirit, during development the developers often singled out as the resource they thought was working best, is generated by striking enemies combo skills and expended using other offensive and defensive skills. The combo skills as of 2010 are listed below. Only the first four retain this function in the final game.
The only known Monk Skills with any boosting effect on Spirit are the combos. Each of these adds a set amount of Spirit to the pool.
Removed combo skills, now with altered functions:
- Dashing Strike -- Combo that allows the Monk to move very quickly across long distances to the enemy.
- Exploding Palm -- Combo that time bombs enemies, triggering them to explode and damage all nearby enemies upon their death.
- Sweeping Wind -- Combo that hits all nearby enemies multiple times.
Monk Spirit Building Passives
- Exalted Soul -- Increases maximum Spirit by 100 and increases Spirit Regeneration by 1 per second.
- Chant of Resonance -- Duration of all Mantras increased by 7 minutes. While one of your Mantras is active you gain 2 Spirit every second.
In 2010 when passives were still called traits, the Monk had one listed that was devoted to spirit regeneration. This ability is no longer in the game.
Spirit was revealed in August 2010, by Game Director Jay Wilson in an interview from Gamescom 2010. 
- Jay Wilson: The Monk has Spirit. That’s the resource we’re happiest with. He came together very quickly. His combo moves generate spirit, and that’s used for signature moves he does. He can’t do them very often. But they’re great attacks, escapes, and some are recovery moves. That one worked out really well.