A blue dwarf is a hypothetical star that is created from a red dwarf star that has exhausted most of its hydrogen fuel supply. Red dwarf stars fuse hydrogen very slowly, and they can allow a large amount of their hydrogen to be fused, which means that the creation of a blue dwarf star takes an incredibly long time.
The idea of a blue star comes from the fact that stars increase in luminosity as they get older. As a star gets brighter, it needs to give off more energy to reach equilibrium. A star that is larger than a red dwarf can do this by getting larger and turning into a red giant, but red dwarfs with very small solar mass are believed to increase their radiative rate and increase their surface temperature to become blue.
Once it exhausts its supply of hydrogen, a blue dwarf becomes a white dwarf and eventually turns into a black dwarf, according to Wikipedia. The blue dwarf star is based on theoretical models, and one has not been found in the universe. The reason for this is because the universe is not old enough to have created blue dwarf stars, which is why they remain hypothetical.