A bastard is, simply put, a child born out of wedlock, something which happened with considerable frequency in period. To be an illegitimate child carried a considerable social stigma in medieval times; bastards, it was believed, were born of lust and carried the "taint" of their nature. For this reason the modern usage of the word "bastard" is typically a derogatory statement implying unpleasant or unreasonable behaviour. Interestingly, in most modern circles illegitimacy does not carry a social stigma, but the usage of the word "bastard" is more popular than ever.
In period, bastards could be acknowledged by their fathers, thus erasing the stain of bastardy.
In heraldry, the bend sinister was a mark of difference denoting that one was a bastard. In SCA heraldry, the bend sinister officially carries no such connotation, but anyone with a bend sinister on their arms can expect some teasing from heralds.