Let's start off by defining introspection more thoroughly.
Ibn Pakudah depicts it as "the act of contemplating your material and
Torah-based circumstances" i.e., your worldly and spiritual standing
identify what you've already done and what you still have to do".
That's to say that we're to begin by surveying our inner and outer
situations dispassionately and impartially; and then we're to speculate
about all the consequences of what we've done, and about what they imply
about the future.
Suppose I notice that I'm selfish, for example (and believe me, we *all*
are to some degree). Then I observe just how much that trait has
interfered with my religious life as well as my relationship with others.
If I were fortunate, I'd then realize that that doesn't bode well for my
spiritual standing, and that I'd hardly likely grow if I continue being
selfish. I'd then want to take steps to be less self-centered.
Ibn Pakudah then provides us with a number of verses meant to inspire us
and shore up our resolve. The most cogent among them seems to be this
one: "Don't be like an ignorant horse or mule" (Psalms 32:9), which is to
say that we're not to just trudge ahead without thinking.
But the one that goes deeper to the core, it seems, is this: "Taste and
see that G-d is good" (Psalms 34:9). Because it seems to set out to remi
G-d is good to us all, despite our errors and notwithstanding all our
false starts. But how can we come to realize that? By "tasting and seeing"
(i.e., experiencing and noting) G-d's goodness in our lives, which we can
also only come to by being introspective, and catching sight of G-d's
presence in the course of each day.