Bias is the error that arises from oversimplified assumptions, and variance is the error that arises from excessive sensitivity to the training data. The bias-variance trade-off is about finding the right level of complexity for a model. Models with high bias may underfit the data, while models with high variance may overfit the data. Ideally, we want to minimize both bias and variance to achieve good generalization. Techniques like regularization and ensemble methods can assist in achieving this balance.

To elaborate further, let's consider an example of a polynomial regression model. A low-degree polynomial (low complexity) will have high bias and low variance; it will tend to underfit the data. On the other hand, a high-degree polynomial (high complexity) will have low bias but high variance, leading to overfitting. The challenge lies in finding the optimal degree of the polynomial that minimizes both bias and variance. This can be achieved through techniques like cross-validation, regularization, or ensemble methods.

Bias refers to the error introduced by approximating a real-world problem with a simplified model, while variance refers to the model's sensitivity to fluctuations in the training data. The trade-off between bias and variance is crucial because reducing one often leads to an increase in the other. High bias can result in underfitting, where the model oversimplifies the problem, while high variance can lead to overfitting, where the model becomes too specific to the training data and fails to generalize well to new data. Striking the right balance between bias and variance is important to achieve optimal model performance.

In the bias-variance trade-off, bias refers to the assumptions made by the model, and variance refers to the model's sensitivity to changes in the training data. In simpler terms, bias is the error from erroneous or overly simplistic assumptions, while variance is the error from sensitivity to small fluctuations in the training set. High bias models are usually too simple, and high variance models are overly complex. To strike a good balance, it's important to choose a model that fits the data well without overfitting. Techniques like cross-validation and model selection can help in achieving the right trade-off.