The bias-variance decomposition essentially decomposes the learning error from any algorithm by adding the bias, variance, and a bit of irreducible error due to noise in the underlying dataset.
Necessarily, if you make the model more complex and add more variables, you’ll lose bias but gain variance. To get the optimally-reduced amount of error, you’ll have to trade off bias and variance. Neither high bias nor high variance is desired.
High bias and low variance algorithms train models that are consistent, but inaccurate on average.
High variance and low bias algorithms train models that are accurate but inconsistent.