Much easier to understand if you know what temperature is
Temperature is proportional to the average energy per particle. Touch a piece of metal on a cold day, and it has lots of cold particles. Your fingers warm them up, and they warm up the ones next to them so it takes a long time to heat the metal under your fingers up to near you body temperature. If you touch a piece of sponge on a cold day, as it is mostly air it has far fewer particles. Air conducts heat badly, so the heat stays near your fingers. Air expands when heated, becomes less dense and floats away drawing fresh cold air into place. Sponge traps air in place, so there are no convection currents. If you touch a piece of metal and a piece of sponge both at 1⁰C at the same time the sponge feels warmer because the part of the sponge in contact with your fingers gets close to body temperature very fast.
Space is almost empty, so its temperature depends on a tiny number of particles. As there are so few particles, there is nothing to conduct heat from on place to another. In a circular orbit, the force of gravity gives precisely the acceleration required to go round in a circle. Everything falls together, so hot air does not rise in orbit and there are no convection currents.
This is a bit of a problem for an astronaut in a space suit. Live humans produce about 100W of heat when idle. If this stayed inside the space suit, the temperature inside would rise until the astronaut died - then it would keep rising until the bacteria decomposing his body died too. You can demonstrate the solution by quickly pumping up a bicycle tyre. The end of the pump gets hot because compressing air increases its temperature. Likewise, when air expands its temperature falls. Space suits pump heat to one place, and let the air slowly leak out there. The hot air carries heat away into space, and its expansion into vacuum cools the space suit.
The last thing we need to understand before we make wee icicles is the boiling point of water. Water molecules attract each other, and that attraction keeps most of them together. The fastest ones can escape from the others and fly off. The fastest ones are the ones with the most energy, so when they go, the average energy per particle falls. Those of you who are still awake will remember that average energy per particle is proportional to temperature, so when some water evaporates, the water left behind gets colder. Evaporation is only half the story. Water molecules in the atmosphere bounce all over the place, and some of them crash into puddles of water. The attraction between water molecules pulls them in hard and increases the velocity, which is a type of energy. When the number of water molecules leaving by evaporation is much higher than the number of water molecules arriving by condensation, the water boils. Reducing the pressure reduces the number of molecules that can arrive by condensation, so the water boils at a lower temperature.
If we still taught physics in school these days, people would understand what happens when an astronaut flushes the toilet. When the urine is piped out into space, the pressure falls and that reduces the boiling point. Boiling pee looses its most energetic particles so its temperature falls until it freezes. As space is almost empty, its temperature does not matter as heat cannot conduct or convect from space to or from the wee icicle. Heat can move in space by radiation. Solar radiation can heat an icicle and that heat cannot escape by convection or conduction into space. The only thing keeping the icicle cool is when the most energetic water molecules leap off into space. Eventually the icicle becomes thin enough to break off without damaging anything.