When an Ashtami (eight day of waxing moon) of sukla pakshna falls on wednesday(Budhavar) it is called Budh ashtami. People pefrom Budh ashtami vrat on these days so that they will never go to hell (Narak).
The story behind being Budh Ashtami as follows:
Once there was a king by the name of Ela in the satya yuga. He was the son of Manu. Ela once he went hunting and while roaming around entered a certain part of a forest and turned into a lady. That part of the forest was protected by the will of Lord Shiva, that if a male entered that part he would be transformed into a lady, as that part was where Goddess Parvati was supposed to visit frequently along with Shiva.
Ela was now a lady and Budha seeing this lady falls in love with her and takes her as his wife, they have a son by the name of Pururuva with whom the Chandravamsa(dynasty of chandra) started.
As the marriage of Budh and transformed Ela took place on the ashtami thiti it is famously known as Budh Ashtami. This day if one performs Budh ashtami vrat he will be free from all the evils he has done and he will be cleansed so that he need not enter hell.