Latches are a lot like D flip-flops, except that instead of a clock they have an enable. When the enable is active, whatever is on the D input is transferred to the internal state and the Q output. When the enable goes inactive, the state will remain what it was the last instant enable was active and the value of D has no effect. So it's very fair to say that data is latched in by the enable.
Some latches omit the /Q outputs as they are not generally required when a latch is needed. Also, omitting them allows the use of a smaller IC package. The 7475 and 7477 are a classic example of this. Each contains 4 single-bit D latches. Notice that enable inputs are shared between pairs of latches.
We've seen a 8-bit latch in part 2 on the logic level input board. On that board a 74373 was used to grab the switch values when the latch button was pressed. That button activated the enable input of the latch. Below is the internal structure of the '373. Note the 8 D latches, and the common active high LE (aka latch enable).
There's one more thing to notice that we haven't talked about yet. Look at those odd inverters on the outputs. They each have a second input. Wait? Wut?
These are tri-state inverters: in addition to the 0 and 1 states we are familiar with, their outputs have a third state.
A logic 0 is essentially connected to ground (through a transistor of some sort usually) and a logic 1 is similarly connected to Vcc. The third state (sometimes called high-impedance) is essentially when the output isn't connected to anything. As such it has no impact on anything else connected to it. This is especially useful when you have a bus with multiple data sources connected to it. Only one can put data on the bus at any time; all the others need their outputs to be in high-impedance mode, i.e. unconnected. In our input board we don't need to worry about that situation so the /OE (output enable) input is connected to ground, enabling the outputs permanently.
We've also seen tri-states on the output board where we buffered the signals using a 74244. We just used it as a buffer to isolate the circuit being observed from the LEDs, but each buffer is tri-state, controlled in groups of 4.