They're small lights controlled by the stage-manager allowing her to cue
stage-crew and front of house operators.

Most people who've used them far prefer cue-lights + headsets to
headsets alone. Many, particularly sound engineers & flymen, are happy
running with just cue-lights

There seem to be two main flavours of cue lights.

The type I'm familiar with seems to be common in the UK. Each remote
cue-light position has a red light, a green light and a button. The
stage manager has a red light, a green light and a three-way switch for
each remote position

The SM moves the switch to 'standby' and both red lights start flashing.
The crewman presses the button to acknowledge and the red lights go to
steady-on. Then the SM moves the switch to 'go', both red lights go out,
both green lights go on. The SM releases the switch and both lights go
out.

These are nice, as the SM has feedback from the crew, and with an
explicit 'go' light it's easy to cue rapid sequences of cues (standby,
acknowledge, go, go, go). The downside is slightly more complex
hardware.

An even better variant of this has separate switches at he SMs desk for
standby and go. The go switch is a three-way, centre-off biased one-way
toggle switch. Moved to the biased position it turns on the go light.
Moved to the non-biased position it transfers control to a master go
switch. This makes it easy to go on multiple crew simultaneously.

The other flavour I know of is a single light at the remote position
with a switch at the SMs desk. These are used on-for-standby followed by
off-for-go, I believe. Anyone familiar with them want to correct me?