I think after reviewing a couple of rules concerning static electricity you'll be able to understand what electric field arrows represent. 

Static electricity is something you're familiar with.  I didn't realize it but there is even a National Static Electricity Day (it was Jan. 9 this year).  Here are some pictures I found online.

A National Geographic Magazine 2013 Photo Contest winner (source)	A cat covered in styrofoam "peanuts" (source).  Being a cat owner I would worry about the cat swallowing one of the peanuts and possibly choking.	I'm not entirely sure what this is.  Is it a dog, is it alive? It is so clean it must never go outdoors. (source)

The static electricity rules are found at the top of p. 59 in the photocopied ClassNotes


Two electrical charges with the same polarity (two positive charges or two negative charges) push each other apart.  Opposite charges are attracted to each other.
 



In this figure  a positive charge has been placed at 3 locations around a center charge.  The 3 charges will all be repelled by the center charge, the outward force exerted on each is shown in blue.  The forces range from weak to strong depending on the distance between the two charges.  

Now instead of drawing in the center charge we have the pattern of electric field arrows that it would produce.


The E field arrows show you what would happen to a + charge at three different locations within the pattern. 
You can also use the pattern of electric field arrows to determine what will happen to a - charge also. 

For a negative charge the force will point in a direction opposite the E field arrow.

We imagine turning on a source of EM radiation and then a very short time later we take a snapshot.  In that time the EM radiation has traveled to the right (at the speed of light).  The EM radiation is a wavy pattern of electric and magnetic field arrows.  We'll ignore the magnetic field lines.  The E field lines sometimes point up, sometimes down.  The pattern of electric field arrows repeats itself.
 

Th picture above was taken a short time after the first snapshot after the radiation had traveled a little further to the right.  The EM radiation now exerts a somewhat weaker downward force on the + charge.

A 3rd snapshot taken a short time later.  The + charge is now being pushed upward again. 
A movie of the + charge, rather than just a series of snapshots, would show the charge bobbing up and down much like a swimmer in the ocean would do as waves passed by.

EM radiation can be created when you cause a charge to move up and down. If you move a charge up and down slowly (upper left in the figure above) you would produce long wavelength radiation that would propagate out to the right at the speed of light.  If you move the charge up and down more rapidly you produce short wavelength radiation that propagates at the same speed.

Once the EM radiation encounters the charges at the right side of the figure above the EM radiation causes those charges to oscillate up and down.  In the case of the long wavelength radiation the charge at right oscillates slowly.  This is low frequency and low energy motion.  The short wavelength causes the charge at right to oscillate more rapidly - high frequency and high energy.

These three characteristics: long wavelength / low frequency / low energy go together. So do short wavelength / high frequency / high energy.  Note that the two different types of radiation both propagate at the same speed.

The following figure illustrates how energy can be transported from one place to another (even through empty space) in the form of electromagnetic (EM) radiation.

You add energy when you cause an electrical charge to move up and down and create the EM radiation (top left).

In the middle figure, the EM radiation that is produced then travels out to the right (it could be through empty space or through something like the atmosphere). 

We spent most of the rest of the class learning about some rules governing the emission of electromagnetic radiation.  Here they are:

1.

Everything warmer than 0 K will emit EM radiation.  Everything in the classroom: the people, the furniture, the walls and the floor, even the air, are emitting EM radiation.  Often this radiation will be invisible so that we can't see it and weak enough that we can't feel it (or perhaps because it is always there we've grown accustomed to it and ignore it).  Both the amount and kind (wavelength) of the emitted radiation depend on the object's temperature.  In the classroom most everything has a temperature of around 300 K and we will see that means everything is emitting infrared (IR) radiation with a wavelength of about 10µm.

2.

The second rule allows you to determine the amount of EM radiation (radiant energy) an object will emit.  Don't worry about the units (though they're given in the figure below), you can think of this as amount, or rate, or intensity.  Don't worry about σ (the Greek character rho) either, it is just a constant.  The amount depends on temperature to the fourth power.  If the temperature of an object doubles the amount of energy emitted will increase by a factor of 2 to the 4th power (that's 2 x 2 x 2 x 2 = 16).  A hot object just doesn't emit a little more energy than a cold object it emits a lot more energy than a cold object.  This is illustrated in the following figure:

The cool object is emitting 2 arrows worth of energy.  This could be the earth at 300 K.  The warmer object is 2 times warmer, the earth heated to 600 K.  The earth then would emit 32 arrows (16 times more energy).

The earth has a temperature of 300 K.  The sun is 20 times hotter (6000 K).  Every square foot of the sun's surface will emit 20⁴ (160,000) times more energy per second than a square foot of the earth's surface.

3.

The third rule tells you something about the kind of radiation emitted by an object.  We will see that objects usually emit radiation at many different wavelengths but not in equal amounts.  Objects emit more of one particular wavelength than any of the others.  This is called  λ_max ("lambda max", lambda is the Greek character used to represent wavelength) and is the wavelength of maximum emission.  The third rule allows you to calculate  λ_max. The tendency for warm objects to emit radiation at shorter wavelengths is shown below.