v1: "At that time," see also 38.1, "in those days;" the attack of Sennacherib preceded Hezekiah's illness. But the king of Babylon heard of Hezekiah's illness. We see both events as tests of Hezekiah's faith; he coped better with Sennacherib's attack than with the Babylonian flattery; sometimes it is the harder things that do us more good, see 38.17.
v2: At the time, Babylon was not the major power. Hezekiah showed his visitors all his treasures, thus making an unholy and unwise alliance. Babylon therefore gained a full inventory of Judah's wealth, for their future invasions.
Since unbelievers cannot understand spiritual things, we are unwise to share fellowship or personal matters with them. We need to be careful who we open our hearts and our homes to. See also 2 Sam 1.20; Matt 7.6.
v3-4: Isaiah questioned Hezekiah, exposing his folly. The Babylonians saw "my palace" and "my treasures" indicating Hezekiah's pride of heart; here was the effect of past victories and present flattery.
v5-7: Babylon, with whom Hezekiah had sought peace, would devastate the land.
v8: Hezekiah could not be responsible for his descendant's unbelief, although he should seek to influence those who came after him.
There is a note of selfish complacency here, as Hezekiah seemed only to be interested in his own things.