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It is one metric to compare models on. a lower log loss value means that the prediction probabilities are closer to the actual 1/0 values (both directionally correct and with a higher degree of confidence). It is helpful to remember that for most model types, classification is a secondary step that uses an arbitrary cut off value. The actual model outputs will be a continuous number bounded 0-1.
For example, logistic regression gives a continuous value like 0.85 as its output. To use it on a classification problem, you would then need to assign a cut off value (such as 0.5) and convert the model output to binary values based on which side of the cut off value they fall.
It's in the name. Loss. You want less loss because you're losing something. In this case, loss = some distance between your predictions and reality. The less distance, the more your model lines up with reality, which is a good thing.
How you define how much representation of reality is lost by your model is up to you. Some common pieces are:
- a minus sign; this is the "purest" measure of distance, on a number line
- some transformation (e.g. squaring); this gives a nice "weighing" for which amounts of loss are negligible and which matter more
- a normalizing piece to shift everything to a nice 0-1 range; this lets us conceptualize the numbers more easily, maybe even use them as probabilities
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