When we take a hot shower it is pretty common to see a white vapour around the bathroom. But the water I am using is below 100º C.
I know the boiling point of the water can be lower than this with a different pressure, but anyway I think I'm at one atmosphere of pressure approximately.
What's the reason for this vapour?
Water and other liquids have a partial vapour pressure, even at temperatures well below their boiling point. At boiling point that vapour pressure becomes equal to the atmospheric pressure and the evaporation manifests itself as bubbles of vapour leaving the bulk of the liquid, a phenomenon known as boiling.
Even at room temperature a saucer of water will evaporate, given some time, due to the relatively low vapour pressure at that temperature. Shower water, say roughly at $50\:\mathrm{C}$, already has a much higher vapour pressure, so the shower generates quite a bit of water vapour, which then condenses in the colder surrounding air, forming a white mist.
Even below $0\:\mathrm{C}$ water has some, limited vapour pressure: see the industrially exploited process of freeze drying.
You will see water condense into clouds of "steam" whenever the relative humidity of the vapor exceeds 100 % (and potential for nucleation exists).
So to see steam in your shower you need two things:
There is a curve of saturated vapor pressure as a function of temperature - I gave the details of this curve in this earlier answer from which I reproduce the graph:
As you can see, at 40 degrees C (hot, but not scalding) the saturated vapor pressure is about 7 kPa; at 20 degrees C (the temperature of the air near your shower) it is only 2.3 kPa. This means that once the vapor given off from the hot water of your shower reaches the cooler air, it will be oversaturated and will have to condense. The condensed water droplets scatter the light, which gives the appearance of steam clouds.
