There are roughly 15 units for each race, which isn’t a lot, but most resources assume that you know what all of them do and how they’re used. I’ll leave the full explanation to Liquipedia (which I highly recommend), but here’s my less than 2 sentence version for each:

Terran

1. SCV – basic worker
2. MULE – specialized workers. Use Orbital Command energy to get these super-fast miners, which are absolutely worth it
3. Marine – basic infantry unit. They’re a little flimsy, but with Stimpack and Combat Shields and in large numbers, they can deal a lot of damage to air and ground units
4. Marauder – heavy infantry. Use their bonus damage against Stalkers, Siege Tanks, Roaches, and other armored units, but note that they can’t shoot up
5. Reaper – harass infantry unit. Scout and harass in the first few minutes of the game
6. Ghost – infantry and caster unit. EMP enemy casters and Protoss armies, and call nukes sometimes
7. Hellion – fast raider car. Sneak them into your opponents base to kill workers or just kill Zerglings on the map
8. Hellbat – transformed Hellion tank. Drop them in your opponent’s mineral lines or put them in front of your army against Zealots and Zerglings
9. Widow Mine – recharging mine. Burrow in critical positions to fire off missiles periodically at workers and clumps of units
10. Siege Tank – a tank. Siege them in battles to do massive splash damage at long range.
11. Thor – massive mechanical unit. Use as anti-air in mech armies and to tank more damage for your Siege Tanks.
12. Viking – transformable flying unit. Long range air-to-air attack while flying to kill Overlords, Brood Lords, Medivacs, Void Rays, Colossi, and more, but they can also land to fight on the ground as well
13. Medivac – flying healing transport. Drop units in your opponent’s base or just keep them with infantry armies to heal them
14. Banshee – flying cloakable harassment. They can only attack ground units, but they do a lot of damage and are very annoying to mineral lines.
15. Raven – flying, detecting caster. Detect invisible units, reduce damage with the point defense drone, and kill clumps of units with the Hunter-Seeker Missile
16. Battlecruiser – flying capital ship. Kill everything in very long games

Protoss

1. Probe – basic worker.
2. Mothership Core/Mothership – flying caster. You can only have one, but it can recall an army back home to retreat or turn a Nexus into a long-range Photon Cannon
3. Zealot – powerful melee unit. They can take a lot of damage and deal a lot if they get in range
4. Stalker – fast ranged unit. Use its mobility (especially with Blink) to harass your opponent and pick off air units
5. Sentry – weak caster unit. Forcefields to trap units, Guardian Shield to reduce ranged damage, and hallucinations for fun and scouting
6. High Templar – caster. Psionic Storm deals massive damage over an area, especially against Terran Marine/Marauder armies and clumped Zerg armies
7. Dark Templar – invisible harass unit. Sneak them into your opponent’s mineral line to harass their economy
8. Archon – powerful tank. It can take lots of damage and deal a lot of splash damage in any composition
9. Observer – a scout. 1 or 2 are useful for detecting invisible and burrowed units and seeing what your opponent is doing
10. Immortal – powerful tank. Use its hardened shields and massive damage to take out Roaches, Stalkers, Tanks, and other armored units
11. Colossus – long-ranged walker that hits multiple units at once. Keep them away from Vikings, but crush any large ground army with them
12. Warp Prism – air transport. Drop and warp in units in your opponent’s base or close to a battle
13. Phoenix – light air harass unit. Pick up and kill workers if you can and get lots to deal with Mutalisks
14. Void Ray – siege air unit. Use its Prismatic Alignment ability to destroy armored units and buildings very quickly
15. Oracle – another light, flying harass unit. It’s used mostly to kill workers at the beginning of games and mostly works solo
16. Carrier – air capital ship. Get them if you’re way ahead and want to shame your opponent
17. Tempest – long range air unit. Mix them in big air Protoss armies

Zerg

1. Drone – basic worker
2. Overlord – flying supply depot. Float them around the map to get more map vision
3. Queen – defensive macro unit. Inject larva for more units, spread creep tumors for more vision and faster movement, and use them for early game anti-air
4. Zergling – fast, weak melee unit. Surround enemy units or run them past the enemy army to do a lot of damage, though they’re extremely fragile
5. Baneling – walking land mines. Run them at Zerglings and infantry armies to destroy lots of units quickly with splash damage
6. Roach – basic tank unit. Use them as the base of an army because they’re pretty tough and very cheap, but they can only attack ground units
7. Overseer – flying detecting caster. Detect cloaked/burrowed units and scout your opponent
8. Hydralisk – glass cannon. They’re weak, but behind Roaches, they can deal a lot of damage very quickly against air and ground units
9. Mutalisk – flying harrass units. Build in large numbers and control them carefully to pick your opponent apart
10. Corruptor – flying anti-air unit. Use the air-to-air attack to counter enemy air armies or to morph into Brood Lords
11. Brood Lord – flying siege unit. They can only hit ground units, but when they do, they spawn broodlings, which also attack and deal tons of damage at long range
12. Infestor – weak caster unit. Fungal growth clusters of enemy units to trap them and deal damage and spit out Infested Terrans for an instant, anti-air army
13. Swarm Host – ground siege unit. Place them far back from a battle and let them spawn Locusts to slowly wear down your opponent
14. Viper – flying caster unit. Charge them up with consume to throw Blinding Clouds on enemy ranged armies or Abduct enemy units with powerful, long-ranged attacks
15. Ultralisk – massive ground tank. Sweep up enemy armies with their area-of-effect attack and tough armor