In XCOM, what are the mechanics for expanding the base (excavating/building)

You can see the full list of Steam achievements at the steam site.

Out of the 60 achievements there are 20 that don't have a description. 10 of them are plot related achievements and you will unlock all of them (except from the Firestorm one) if you finish the original game:

• Prisoner of War: Capture a live alien.
• The Gatekeeper: Stun an Outsider.
• X Marks the Spot: Uncover the alien base's location.
• Off My Planet: Recover the Hyperwave Beacon.
• Ride the Lightning: Build a Firestorm. (not essential for the plot)
• See All, Know All: Build the Hyperwave Relay.
• Beyond the Veil: Find a soldier with the Gift.
• And Hell's Coming With Me: Successfully assault an Overseer UFO.
• On the Shoulders of Giants: Build the Gollop Chamber.
• The Volunteer: Make contact with the Ethereal hive mind.

UPDATE:

There are 10 more that don't have a description, 5 of them are related to the slingshot DLC, those are:

• New Friend: Complete Friends in Low Places.
• Bait the Hook: Complete Confounding Light.
• The Bigger They Are: Complete Gangplank.
• Rising Dragon: Take your new ally into the final challenge.
• All Aboard: Complete Confounding Light with more than 3 turns left on the timer.

The other 5 do not appear on the xbox 360 version or the PS3 version, and have 0% completion, which means that nobody was able to get them, just as it was with the above 5 before the release of the slingshot DLC, those are:

• Disaster Averted: Complete Deluge.
• The Chase Is On: Complete Portent.
• Great Minds Think Alike: Complete Furies.
• No Sweat: Complete Deluge without activating more than 2 valves.
• Saved to Savior: Have your newest ally volunteer for the most difficult duty.

As you can see, their description, taken from here, makes no sense regarding to the game. With the history regarding the slingshot DLC they are probably related to a future DLC.

Hero units are created by specifying their first and last name in the barracks "Customize" screen. Once you do this, your soldier will be replaced by the hero unit. These units are considered to be cheats, though, as they are super-powered. They have high stats and start with advanced gear. You will be notified when you specify a hero's name that achievements are disabled as a result.

Also note that customization of these heroes is disabled - you can't change their names or any of the other options on that menu (armor color, armor type, gender, etc). You can also take their gear, but your other soldiers can't use it without doing the appropriate research.

You can summon as many clones of each hero as you choose. If you want to field a team of all Sid Meier clones, you are free to do so.

There are four confirmed heroes so far:

• Sid 'Godfather' Meier - one of Firaxis' founders, and legendary game designer
• Ken 'Big Daddy' Levine - co-founder of Irrational Games, who developed Bioshock
• Joe 'Archangel' Kelly - a comic book writer for Marvel
• Otto 'Unbreakable' Zander - a reference to a popular XCOM Let's Play series by GuavaMoment.

(I'm providing their nicknames for flavor, you don't have to specify them when you customize your character.)

These names are given in the game's files, you can find them in:

(Steam Folder)\steamapps\common\XCom-Enemy-Unknown\XcomGame\Localization\INT\XComStrategyGame.int

Search this file for "SuperSoldierFirstNames" and you'll come across all four, in addition to the strings that prompt you when you enter their name.

Here's Otto, note his 100 HP, Will, and Aim:

Kotaku also has a video guide which shows off summoning Sid himself, as well as Ken Levine.