Q:

Powering an object with a relay (has continuity but it doesn't seem to be delivering any current)

I am trying to learn how to control a relay to power various household objects. I bought a power relay shield for an adafruit feather huzzah (esp8266), and I have just set up the arduino blink sketch to provide conditional high / low to a control pin on the relay:
const int ledPin = 13;

void setup() {
  pinMode(ledPin, OUTPUT);
}

void loop {
    digitalWrite(ledPin, LOW);
    delay(1000);
    digitalWrite(ledPin, HIGH);
    delay(2000);
}

If I connect a jumper from the signal pin hole on the board to the appropriate ledPin (13), I can hear the relay switching on and off. If I use a multimeter in continuity mode, it will register continuity at the appropriate times in the blink sketch (HIGH or LOW).  
I might be confused on how the relay should be wired, but shouldn't attaching wires from two of the terminal blocks deliver power to something? If I use a multimeter on wires coming out of the blocks, I don't detect any current. I've tried powering a simple led, but I can't get it to light up. Here's my setup. Can anyone explain what I might be doing wrong? Does the LED need a separate power source apart from what's coming from the feather itself? (the feather is powered by a USB cable from my computer).
Thanks for any clarification anyone can provide.

Here is a reference photo of how adafruit has things wired.

Here's an update of my implementation - let me know if anything looks wrong/dangerous. Thanks!

A:

Thanks for the picture. From what I can see, your wiring is wrong, possibly because your mental model of a relay is wrong.
The relay will connect the center post to one or the other posts. One output is called "normally closed" and is connected to the center when the relay is not energized, the other is called normally open and is connected to the center post when the relay is energized.
so your circuit is basically this:

simulate this circuit – Schematic created using CircuitLab
This schematic should make it obvious why there is no current going through your LED.
edit this is one way you could make it work:

simulate this circuit

