Naive Bayes Classifier, Explain model fitting and prediction algorithms

Naive Bayes Classifier, Explain model fitting and prediction algorithms

I have the two equations below that relate to the model fitting and
prediction algorithms of a naive bayes classifier.
I am trying to understand what line 6 of algorithm 3.2 is doing. I think
it is trying to make the numbers "nicer" by doing the log-sum-exp trick,
which I still don't understand fully. Could someone outline why this
is/needs to be done? And specifically what the argument to the
logsumexp(Li,:) means/is/reads as?
Also could someone give me a good notion of what the two values in line 8
of algorithm 3.2 is for? Are they basically initial offsets/biases to the
Lic in algorithm 3.2?

From Machine Learning A Probabilistic Prospective Author Kevin P. Murphy