TM 01 Mega Punch Powerful Physical Attack
TM 02 Razor Wind (Can someone please give me a description of what this does!)
TM 03 Swords Dance Raises Physical Attack
TM 04 Whirlwind Blows Away Opponents
TM 05 Mega Kick Powerful Physical Attack
TM 06 Toxic Best Poison Attack
TM 07 Horn Drill (And what this does)
TM 08 Body Slam Physical Attack. Possible paralysis on enemy
TM 09 Take Down Physical Attack With Slight Rebounding Damage
TM 10 Double Edge Physical Attack With Slight Rebounding Damage
TM 11 Bubble Beam Strong Water Attack
TM 12 Water Gun Medium-strength Water Attack
TM 13 Ice Beam Powerful Ice Attack
TM 14 Blizzard Extremely Powerful Ice Attack
TM 15 Hyper Beam Extremely Powerful Dragon Attack
TM 16 Pay Day Attacks And Takes Money Of Opponent
TM 17 Submission Physical Attack With Slight Rebounding Damage
TM 18 Counter Counter Attack
TM 19 Seismic Toss Ground Attack
TM 20 Rage Repeated Physical Attack. Does More Damage As Pokémon Is Attacked. No Control Over Pokémon
TM 21 Mega Drain Powerful Plant Attack. Heals You By Half The Amount Of Damage You Did
TM 22 Solar Beam Extremely Powerful Plant Attack. Takes One Turn To Charge Before Unleashing
TM 23 Dragon Rage Powerful Dragon Attack
TM 24 Thunderbolt Strong Electric Attack
TM 25 Thunder Extrememely Strong Electric Attack
TM 26 Earthquake Strong Ground Attack
TM 27 Fissure Instant Knock Out. Ground-type.
TM 28 Dig Strong Ground Attack. Pokémon Goes Underground First Turn, Then Attacks.
TM 29 Psychic Strong Psychic Attack
TM 30 Teleport Teleport Out Of Battle. Doesn't Work In Trainer Battles.
TM 31 Mimic (And what this does.)
TM 32 Double Team Raises Pokémon's Evade.
TM 33 Reflect (And, finally, what this does.)
TM 34 Bide Absorbs damage you take and returns it with double force.
TM 35 Metronome Randomly Does one move out of the entire repertoire of pokémon moves.
TM 36 Self-destruct Destroys User And Deals Damage To Opponent.
TM 37 Egg bomb Attacks repeatedly. Grass-type
TM 38 Fire Blast Strongest Fire Attack. Misses 1/4 Of The Time.
TM 39 Swift Extremely Accurate Attack. Never Misses, Even If Opponent Is Up In The Air Or Underground
TM 40 Skull Bash Strong Physical Attack. Takes one turn to charge before unleashing.
TM 41 Softboiled In Battle - Heals Chansey. Out Of Battle - Takes Away Chansey's HP And Gives It To Another Pokémon, Doubled. Only Used By Chansey. (Or Mew, If You Are Lucky Enough To Find It)
TM 42 Dream Eater Attacks sleeping Pokémon
TM 43 Sky Attack Extremely Strong Flying Attack. Takes One Turn To Charge
TM 44 Rest Heals User's Status, Puts User To Sleep
TM 45 Thunder Wave Paralyzes Enemy. Electric-type
TM 46 Psywave Extremely Strong Psychic Attack
TM 47 Explosion Destroys User, Deals Damage To Opponent. Stronger Than Self-Destruct
TM 48 Rock Slide Strong Rock Attack.
TM 49 Tri-Attack Physical Attack.
TM 50 Substitute Creates Doll To Take Damage. No Status Ailments While Doll Is Out. Takes Some Of Pokémon's HP To Create Doll.

TMs 51 - 55 are the same as HMs 1 - 5. See the HM section to see what they do.

I did more than two/thirds of this list personally and used another resource from the web to complete it.