A model is trained by reducing a loss function on training examples. After a set of updates, the same loss can be measured on data not used to update the parameters. That held-out measure is validation loss.
When training loss falls but validation loss rises, the model may be overfitting: getting better at its training material while generalizing worse. Researchers use validation trends to select checkpoints, tune settings and decide when to stop.
Loss depends on the prediction task, tokenizer, weighting and dataset. It cannot be compared fairly across unrelated setups without checking those details. In language modeling, cross-entropy loss is often used, while perplexity is a related summary derived from that loss.
Keep validation data separate from training and report its source and size. Monitor rare-case performance too, because a single average can hide degradation in the tails.