Both bias and variance are errors. Bias is an error due to erroneous or overly simplistic assumptions in the learning algorithm. It can lead to the model under-fitting the data, making it hard to have high predictive accuracy and generalize the knowledge from the training set to the test set.
Variance is an error due to too much complexity in the learning algorithm. It leads to the algorithm being highly sensitive to high degrees of variation in the training data, which can lead the model to overfit the data.
To optimally reduce the number of errors, we will need to tradeoff bias and variance.