What is a latching circuit?

latching means the component or circuit has two stable states, and some signal will cause the circuit to change from one to the other state. This can be a flip-flop, a memory cell, a latching relay, or other.

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A latch is how electronic devices remember.

A simple relay closes it's output contacts whenever power is applied to it's coil. When the power goes away, the contacts open. No memory. Just a dumb relay.

HERE IS YOUR APPLICATION: you want to know whenever anyone comes in your room when you are gone. So, you put a floor pressure mat switch under the rug. You want the relay to energize when someone steps on the mat, and to stay energized until you reset it.

So, you wire your power source in series with the pressure mat switch to the relay. But like the first example, it still has no memory. Now, connect the normally open set of relay contacts in parallel with the pressure mat switch. Now, when the stepped on, it activates the relay, but when the foot is removed, the relay contacts hold the relay activated... at least until you remove the power. (See the link below.)

That is a 1-bit digital memory. A solid state latch is much smaller, and your computer has billions of these latches in it, storing programs it is running and data. All electronic computer memory is just many, many latches connected together.

In electronics, a latch is a kind of bistable multivibrator, an electronic circuit that has two stable states and therefore can store one bit of information. Today the word is mainly used for simple transparent storage elements, while slightly more advanced non-transparent (or clocked) devices are described as flip-flops.

Latches are designed to be transparent. That is, input signal changes cause immediate changes in output.