Geocaching is the real-world treasure hunt. There are over 2 million active geocaches and over 6 million geocachers worldwide.
Participants navigate to a specific set of GPS coordinates and then attempt to find the geocache (container) hidden at that location.

When you go to geocaching.com and put in an address or longitude/latitude you get a list of nearby geocaches.
See:
Geocaching > Geocaching 101
What is Geocaching? - YouTube

A geocache may be a simple small cylindrical container the size of a bolt with a rolled up log sheet.
More likely it is a tupperware style box with trinkets and a log book. You can take a trinket and replace it with one of equal value or simply sign the log.
It may also contain a travel bug® (see below) or geocoins which have tracking ID numbers.

Search Rules:

1. If you take something from the geocache (or "cache"), leave something of equal or greater value.
2. Write about your find in the cache logbook.
3. Log your experience at www.geocaching.com.

Example from Groundspeak (geocaching.com) for Duke Farms in NJ
(Click on images for an interactive version)
See: Geocache Types

Images from c:geo app
Traditional Cache - the most basic type: a box and a log book.
Multi Cache - Two or more locations each one leading to the next.
Mystery or Puzzle Cache - Require you to solve a puzzle to determine the final coordinates.
Earth Cache - Not a geocache box to be found, but instead notes on geological features and noteworthinesses.
Virtual Cache - box-less geocaches. You may be required to answer a question about the location, take a picture, complete a task, etc...
Wherigo Cache - play a story using your [GPS] receiver and find a geocache box.
Event Cache - organized gathering for and by geocachers, sometimes regular events.
Cache In Trash Out Cache - another variation of event caching where you pickup trash while geocaching to improve the environment.
Mega Cache - large events.
Letterbox Cache - a letterbox with stamp, optionally containing trade items.
Webcam Cache - a public webcam with no box, logbook, or trade items. Finders are typically required to proof their find by capturing an image from the webcam.

        You can also get a map.                                           Click on a cache to get details
   
Half way down on the page for a cache you will see "Additional Hints (Decrypt)". Click for more hints.

According to the "What does a geocache look like?" section Groundspeak's Geocaching Guide Geocaching 101, cache sizes are defined as:

• Micro - Less than 100ml. Examples: a 35 mm film canister or a tiny storage box typically containing only a logbook or a logsheet. A nano cache is a common sub-type of a micro cache that is less than 10ml and can only hold a small logsheet.
• Small - 100ml or larger, but less than 1L. Example: A sandwich-sized plastic container or similar.
• Regular - 1L or larger, but less than 20L. Examples: a plastic container or ammo can about the size of a shoebox.
• Large - 20L or larger. Example: A large bucket.

Caches containers can be pretty sneaky with many disguises.
     
lock & lock                Gum           Bolts          Rocks   Bison micro camo  Nano w/ magnet
      
  Reflector      Pelican Container  Ammo Can (small)     Pine Cone          Small Log 
  

Sites where you can log caches
Groundspeak geocaching.com the Grandaddy
NaviCache
Earthcache - Promotes earth science education
See others at Geocaching websites - Cacheopedia

Hiding Rules:

• Don't hide on private property
• Geocache placements do not damage, deface or destroy public or private property.
• Check with any relevant agency (e.g. USDA Forest service) before placing caches.
• Caches in or near military installations are not allowed
• Geocache containers should be waterproof and durable.
• Camouflage the container. This is optional but a good idea, as you don't want non geocachers finding it.
• Label the outside. In today's world, suspicious packages can create alarm.
• Geocaches are never buried, neither partially nor completely.
• Physical elements of different geocaches should be at least 0.10 miles (528 ft or 161 m) apart.
• Stock the cache. Include a letter explaining what it is, in case a non geocacher finds it.
• Make sure you have a good satellite signal, then let your GPS settle at the cache site for a minute or two before marking. Come back 90 minutes later and average the two readings.
• Try to hide it where searchers won't be observed by homeowners or passersby. This lessens the likelihood of someone reporting suspicious activity or removing the cache.
• Contents are family-friendly.
• Geocaches do not solicit for any purpose.

BYOP - Bring Your Own Pen/Pencil. 
Camo - Camouflage
CITO - Cache In Trash Out is an ongoing environmental initiative
      supported by the worldwide geocaching community. Since 2002,
      geocachers have been dedicated to cleaning up parks and other
      cache-friendly places around the world. 
DNF - Did Not Find.
D/T - Difficulty and Terrain rating. e.g. 2/3 - Difficulty=2, Terrain=3 out of 5
FTF - First to Find
GC Code - A unique identifier associated with every geocache listing.
Geocoin - A Geocoin works similarly to a Travel Bug (see Travel Bug) in that they are trackable
and can travel the world, picking up stories from geocache to geocache.
Geocoins are often created as signature items by geocachers and can also be used as collectibles.
GPX - GPS eXchange file
LOC - GPS location file
Latitude - 
Longitude - 
Muggles - People who are not geocachers
RITR - Rite in the Rain Logbook
TB - Travel Bug® - A Travel Bug is a trackable tag that you attach to an item.
TFTT - Thanks for the Trackable
SL - Signed Log
TFTC - Thanks For The Cache.
UTM - Universal Transverse Mercator - A worldwide location identification system.
   Based on the mercator projection mapping dividing the map up into rectangles
Muggle - A non-geocacher. Based on "Muggle" from the Harry Potter series,
             which is a non-magical person.
 - Regular Cache
 - Puzzle Cache - Has a puzzle you have to solve to find the actual cache.
See:
Glossary  of Terms - Geocaching.com
Glossary - Cacheopedia

Links:
Cacheopedia - Cacheopedia
Geocaching.com
  Geocaching 101   Geocache Types GEOCACHING | OffTheGridCaching.com
GPS GPS devices in products
Geocaching Apps for your smart phone or tablet
GPS technology under tech
Map Coordinate Systems
Cache containers at WorldCaching.com