Electronic – n implicit “unit of time” involved in electricity measurement? (e.g. miles per hour, kb per second, amps per ???)

I'm very new to electronics and I am going through what must be a common difficulty in grasping voltage, current, and resistance. I'll restrict my question to current as I suspect understanding that piece may shed light on voltage and resistance.

I've read a few questions here:

• Help with understanding Current, Voltage and Resistance

• Understanding voltage and current

And they helped a bit but I'm still struggling. One specific part that's difficult for me to resolve mentally is that I am reading about the basic units of measurement, but I'm not entirely sure what is being measured. For example, a pound is measuring the force of gravity pulling on a collection of atoms. A gallon is the amount of liquid that can occupy a fixed amount of space. Electricity… I get lost on the details of what's being observed.

Many units of measurement are a fixed quantity of something that does not change (unless acted upon). For example:

• 1 Gallon of milk
• 16 ounces of beef
• 30 cubic liters of air

That doesn't seem to make sense with something like current that is measuring electrons constantly in motion. Alternatively we perform measurements of something as it changes over time:

• 35 miles per hour
• 128 kilobits per second
• 5,000 gallons per minute

When it comes to current, we just say "amps", not "amps per something". Well, I get that "amps" measure the flow of electrons, but what exactly does that "flow" mean? Is it the number of electrons (or the number of something else) passing through a location on a circuit in a second (or some other unit) of time? When I touch the leads of my multimeter to a wire, what exactly is it "looking at"?

I've read that volts are a measure of potential energy related to joules and coulombs (http://www.allaboutcircuits.com/vol_1/chpt_2/1.html) (more confusion but that's fine) and I believe that coulombs are measured per second. Does the per-second carry over to amps as well?

The only other thing I can think of is that amps might be more like pressure where you're measuring pounds per square inch.

I know electricity is electricity and no analogy is perfect. I'm trying to understand electricity for what it is, I'm just not sure how these measurements are actually made. Perhaps I'm overthinking, but any deeper insight would be great.

(If this has already been explained to death I apologize, I may not know the best search term to use.)

Man, as someone new to this site I'm so blown away that so many people took so much time to help me understand this. Like a lot of things I think it's going to take time and a lot more reading / experience to "sink in" but all of the answers were so helpful. I'm marking the "amps include time" answer as the one that helped me the most because it answered the core of my question "amps per what?". I'm picturing "amps" kind of like "knots" in the sense that the quantities are part of the definition of the word as opposed to being explicitly stated as they would be in another unit like "miles per hour". Not a perfect analogy but at least it helps me understand where all the hard numbers went.