The Gregarious Railfan
Understanding Railroad Signaling
The motherlode of railroad signalling information regarding aspects and indication is
Todd Sestero's
Signal Aspects from the Rulebooks page from his complimentary website
RAILROAD SIGNALS of the U.S.      
In short, don't expect to quickly learn all the idiosyncrasies of railroad signaling from the charts that will be shown in
the above website. The terminology takes a little getting used to.  The beginning terms to learn are 'Aspect' and
'Indication'. And railroads have not standardized signaling yet but that is coming.
'Aspect' is the arrangement of the number and color of lights on the signal.
'Indication' is what that combination of lights and colors tells the engineer in how to proceed.
First thing a railfan needs to know is ALL RED means STOP; everything else means GO the differences are how fast
and which way.  The word 'diverging' crops up frequently, and means 'diverge' from the main onto a siding or turnout.
There are four colors used Red, Yellow, Green, and Lunar (White).  Lastly the terminology for speeds is as follows
from slowest to fastest (as far is I can gather) - stop, restricting, approach, slow, and proceed at track speed.
Again, this is where it pays to be gregarious, other railfans are the fountain of information that can open up the
understanding of railroad signaling.
I have Found two sets of videos on YOU TUBE explaining Signaling;
one set of 4 by Ian Juby and one set of 5 by Distant Signal.
Both are good primers if you want to learn how to read signals:
Want to learn even more about U.S Railroad signals? Dive
into Todd Sestero's Railroad signals website.
Here are some definitions of 'indications', there are more. Different
railroads will have more or fewer 'indications' according to their own needs.
SIGNAL ASPECTS of the AT&SF RWY CO. (typical)

Clear  - Proceed

Approach Limited – Approach prepared to pass next signal not exceeding 60
mph and prepared to advance on diverging route

Advance Approach  - Approach prepared to pass next signal not exceeding 50
mph and prepared to advance on diverging route

Approach Medium - Approach prepared to pass next signal not exceeding 40
mph and prepared to advance on diverging route

Approach - Proceed prepared to stop at next signal, Trains exceeding 40 mph
immediately reduce to that speed

Approach Restricting - Proceed prepared to pass next signal at restricted speed

Diverging Clear –  Proceed on diverging route not exceeding prescribed speed
through turnout

Diverging Approach - Proceed on diverging route not exceeding prescribed speed
through turnout.  Approach next signal prepared to stop, if exceeding 40
mph immediately reduce to that speed

Restricting – proceed at restricted speed

Stop - Stop
Since this page was created, TRAINS Magazine has published a great
article explaining railroad signalling in their January 2016 issue  TGR