Two points in a circuit are considered to be “open” when there isn't a path for current to flow between them. This occurs when the resistance between the points is effectively infinite so that current cannot flow. (Resistance is a measure of a circuit's or component's ability to impede the flow of current. Ohm's Law says the current $I$ is given by the voltage $V$ divided by the resistance, $I=V/R$. For a fixed voltage, the greater the resistance, the less current will flow. When the resistance is infinite, the current is zero for any finite voltage because dividing a finite number by infinity yields zero.)
Air is a very poor conductor of current and is often approximated as having an infinite resistance. Thus, in a circuit where the current would have to move through air in order to “complete the circuit,” the circuit is said to contain an open or to be an open circuit. (By “complete the circuit” we mean starting at some point in the circuit and then moving through any number of components and wires to return back to the starting point without retracing any portion of the path.)
Opens often occur when components physically break or when wires are not connected in the intended manner. Opens are a common cause of problems in a circuit, so it is important to recognize when they occur. Fortunately, it is often easy to fix an open: frequently the fix merely requires that one reattach a disconnected wire!
Figure 1 shows a simple circuit without an open—there is a complete path for current to flow. Figure 2 shows the schematic representation of this circuit. The entire “top” wire—between the positive terminal of the battery and the top of the resistor—is at a potential of 3V.
Provided there is a path for current to flow, current in a circuit such as the one shown in Fig. 1 will flow from the positive terminal of the voltage source (battery) to the negative terminal. In Fig. 1 we see that current travels in a clockwise direction around the circuit. The current passes through the resistor and the battery uses a chemical process to move the current/charge from the negative terminal back to the positive terminal (this chemical process raises the potential of the charge). Thus this circuit provides a complete path for current to flow.
Figure 2 shows the same circuit except now there has been a break in the wire between the resistor “R1” and the positive terminal of the voltage source. That break is acts as an “open” in the circuit, i.e., it can be thought of as having infinite resistance.
For the circuit in Fig. 3, the voltage measured directly across the voltage source (with respect to ground) is still what it was before the break appeared. For example, if the voltage source was a 3-volt battery, measuring the voltage difference between ground and any point on the top wire between the positive terminal and the break would still show 3V. However, points beyond the break, i.e., points to the right of the break and up to the top of the resistor, would have a potential of 0V. These points are equivalent to ground because, with the break in place, there is nothing trying to “push” charges from the top of the resistor to the bottom. Because the bottom of the resistor is connected to ground and there is no difference in potential across the resistor, both ends of the resistor are at the same potential of 0V. While there is still a voltage difference in the circuit (it appears across the infinite resistance of the break), current no longer flows. If one were to measure the resistance across the break, it would read as infinite. (On most digital multimeters infinite resistance is displayed as “overload.” This is what the meter displays for points that are not electrically connected.)
A broken or disconnected wire can often be quickly identified as the source of an open circuit. However, sometimes opens are less obvious. For example, a failed component, such as a burned-out LED, may act as an open while showing no obvious signs of having failed (other than the LED not illuminating in the case of a burned-out LED).