A machine learning model that performs poorly can be failing in one of two genuinely opposite ways, and figuring out which one matters enormously, because the fix for one failure mode often actively worsens the other. A model can be too simple, unable to capture the real underlying pattern in the data at all — a failure mode called high bias, or underfitting. Or it can be too complex, capturing not just the real pattern but also the random noise specific to its training data — a failure mode called high variance, or overfitting. The bias-variance tradeoff describes the genuine tension between reducing one of these failure modes and inadvertently increasing the other.
Underfitting misses the real pattern entirely
An underfit model is too simple, or too constrained, to represent the actual relationship present in the data — trying to fit a straight line through data that genuinely follows a curved pattern, for instance. This kind of model performs poorly not just on new, unseen data but even on the very data it was trained on, since it simply lacks the flexibility to capture the real underlying pattern at all, regardless of how much training data it's given. High bias, in this technical sense, refers to the model's outputs being systematically, consistently off from the true underlying pattern in a predictable direction, because the model's own structure is too rigid to represent that pattern accurately in the first place.
Overfitting captures noise along with the real pattern, and neither generalises well
An overfit model sits at the opposite extreme: it's flexible enough to fit its specific training data extremely closely, including the random noise and quirks specific to that particular training sample, not just the genuine underlying pattern the model is actually meant to learn. Such a model can look impressively accurate on the exact data it was trained on, while performing considerably worse on new data it hasn't seen before, because it's effectively memorised noise specific to the training sample rather than learning the genuinely generalisable pattern underneath it. This is why simply making a model more complex to fix underfitting, or more constrained to fix overfitting, isn't a free lunch: pushing a model toward greater flexibility to better capture a genuinely complex real pattern also increases its capacity to fit noise, and pushing it toward greater simplicity to avoid fitting noise also reduces its capacity to capture a genuinely complex real pattern — the two failure modes trade off against each other, and effective model design is fundamentally about finding a workable balance between them, not simply eliminating both by making a model arbitrarily more or less complex.
What we're still unsure about
The bias-variance tradeoff itself is a rigorously established, mathematically well-characterised concept in statistical learning theory, not a matter of genuine dispute. What requires real practical judgement, rather than a fixed formula, is finding the actual right balance point for a specific real model and dataset, since the ideal tradeoff point depends on factors like how much training data is actually available and how much genuine underlying complexity the real relationship being modelled actually has — quantities that aren't fully known in advance for a new, unfamiliar problem, which is why practitioners typically rely on techniques like cross-validation, testing a model's performance on held-out data, to estimate empirically where that balance point actually falls for a given specific problem, rather than being able to calculate it directly from first principles alone.
This sits inside Model Evaluation & Bias-Variance Tradeoff, one of eight topics in AI/ML, one of seven domains in Computer Science, one of seventeen subjects the app can quiz you on.