The campaign logs are glowing silver spheres that are hidden in all the campaign missions. They can be collected by walking or driving an appropriate unit into them.
Since there are 24 total, you only need 12 for this achievement, and a regular play-through of the campaign will most likely get you at least 12 even if you aren't looking everywhere for the logs.
They are fun to look for and collect, and also give you extra Halo story which I very much enjoyed!
If you are going to go for all 24 on your first run through, and you want the fun of the hunt, look EVERYWHERE in every mission! However, be warned, you do have to complete some optional objectives or destroy something in a few cases to get the log!
If you want to know how many are in a mission without knowing where they are:
Campaign logs per mission:
Or perhaps you want the full details!
Campaign logs by location in each mission:*** Spoiler - click to reveal ***All credit for this writeup goes to the unknown author on gameranx. I couldn't figure out who wrote it so can't give direct credit at this point.
Mission #1: The Signal
Log #1: Found on the ground, right before destroying the makeshift defensive wall. You can’t miss it.
Log #2: After driving through the wall of cars, continue up the road. As you reach the research buildings, you’ll find the log on the road, right in your path.
Log #3: Next to the research building in the center of the area.
Log #4: Right before the light bridge.
Log #5: Cross the bridge, and you’ll find this log next to the crash site where you’ll find the recon team.
Log #6: Use the portal, and you’ll find this log at the fence.
Mission #2: A New Enemy
Log #7: At the start of the mission, wipe out the first group of enemies, then look near the waterfall in the area.
Log #8: Once you destroy the enemy base, you’ll be able to call in a base of your own. Right behind the enemy base, collect the glowing log.
Mission #3: Ascension
Log #9: Up the hill from the light bridge, there’s an area with a log and some resource piles.
Log #10: Fight up to the Objective C marker and explore up the forerunner structure.
Mission #4: One Three Zero
Log #11: North of the group of soldiers you rescue early in the mission.
Mission #5: The Cartographer
Log #12: Located behind the first forerunner conduit you’re ordered to destroy.
Log #13: Destroy the east and west base before going for the northern (and final) conduit. This optional challenge unlocks the log and the skull.
Mission #6: Lights Out
Log #14: Destroy the enemy base by the final portal. After the base is destroyed, the collectible is floating over the ruins.
Log #15: Move south from that enemy base to the middle of the map. There’s a hill with prisoners to free and resource pick-ups.
Mission #7: From the Deep
Log #16: Explore the eastern side of the map. The log is near the unit of marines.
Mission #8: Hold the Line
Log #17: Go to the enemy spawn area in the northeastern edge of the map. You’ll find the log there.
Log #18: Find the smaller base location in the southwestern corner of the map. The log is to the left.
Mission #9: Under the Dark
Log #19: Move to the far northeastern corner and past the Kodiaks to find an alcove on the right. Between the two blast walls, there’s a log to pick up.
Log #20: Kill all three Brute Warlords to complete an optional challenge. This will unlock a log and a skull.
Mission #10: The Foundry
Log #21: Search the area to the left of the Scarab wreck.
Log #22: Find the small enemy base south of your HQ and destroy it to uncover a log.
Mission #11: The Halo
Log #23: Right next to your starting base.
Mission #12: Last Stand
Log #24: After gaining the objective to kill the warlords, check the right side of the area