Definition of 'Homoskedastic'
A statistics term indicating that the variance of the errors over the sample are similar. This type of error structure is most often assumed in statistics, but is not always the case when regression is done. If the variance of the errors around the line of best fit varies much, it will not show a pattern or tendency.
Investopedia explains 'Homoskedastic'
For example, in a homoskedastic sample, the variance of errors will not increase when the variables increase.
Suppose you took a sample population of people, some with very high incomes and others with very low incomes. For the variance to be considered homoskedastic, the magnitude of the errors for each term compared to the line of best fit would need to be about the same for each person, regardless of the magnitude of his or her income. In reality this isn't likely to be the case very often.