What Information Is Gleaned From Conducting An Apple Hardware Test?
As Thecafremo stated in the first answer, AHT/Apple Diagnostics will only show &quot;No trouble found&quot; or provide you with an error code assuming it detects a failure.
Apple Hardware Test (AHT) essentially runs minor stress tests on the major internal components and sensors in your Mac.  The standard AHT test runs quick memory tests, fan tests, Mac wide sensor tests and a very brief hard drive read/write &amp; SMART status test.  AHT also has a checkbox for an extended test, which runs the same tests as before but expands it's memory &amp; hard drive tests, running full pattern tests on RAM and a longer disk scan on the hard drive.  The extended test takes a significantly longer amount of time, 1+ hours compared to 5~ minutes, than the standard test.  While it runs you will hear your different fans spin up to full speed for a few seconds and a progress indicator on the screen tells you what component it is currently testing.  Assuming no failures are found it will present a &quot;No trouble found&quot; message once it's finished.  If failures ARE found then AHT will return a cryptic error code that can be deciphered using the info below, pulled from an excellent CNET article:

4ETH: Ethernet controller
4IRP: Main Logic board
4MLB: Logic board controller
4PRC: Processor
4HDD: Hard disk
4MHD: External disk
4YDC: Video card
4SNS: System sensor
4MOT: Fan motor
4MEM: Memory module
4AIR: AirPort wireless card

The below info, pulled from the same CNET article, can help you isolate specific sensors when the 4SNS error is returned.  The first letter should either be L for current, T for temperature or V for voltage, indicating the type of sensor. The second letter (A, e, M, etc) refers to the component area where the sensor is located.  So, using this along with the info below, we can assume that 4SNS....TH.... error would be the hard drive's temperature sensor.

A: Ambient air sensor
B: Battery
C: Central processors (CPU)
D: DC (direct current)
e: PCI-express slot
F: FireWire port
G: Graphics processor (GPU)
H: Hard disk
h: Heat pipe (heat sink)
L: LCD display
M: Memory or memory riser boards
m: Misc. (i.e., battery chargers)
N: North bridge (motherboard controller)
O: Optical drives
P: Power bus
p: Power supply
s: Palm rests for laptops
W: Airport Wi-Fi card

Apple Diagnostics, available on mid-2013 and newer Macs, runs essentially the same small stress tests as AHT but will return more human readable messages based on it's findings.  If errors are detected it will explain in terms along the lines of &quot;There appears to be a problem with your hard drive&quot; but can still return a cryptic reference code.  Apple Diagnostics gives you the option to reboot to your recovery disk though and to contact Apple's support site for options on resolving any errors found.