v1: The dating of Hosea, see Is 1.1, who is one of his contemporaries. The dates refer both to Judah and Israel, for much is addressed to both kingdoms. Like Isaiah (Is 8.18) the prophet and the message are intimately linked; he is the message.
At this time, God raised up writing prophets (Isaiah, Micah being the first), so that their message be preserved. Other prophets, such as Elijah and Elisha, did not write.
v2: The theme of the book is Judah's and Israel's unfaithfulness to God; both departed from the Lord, and committed 'spiritual prostitution.' Hosea's message was delivered by word, but also by his life. Thus, he takes an "adulterous wife," illustrating Israel's persistent unfaithfulness. Hosea lived during a time of political instability in the Northern Kingdom; see 2 Kings 14-15.
v3: Hosea obeyed his call, and took a prostitute as wife. Marriage in this way would bring great shame on Hosea, and doubly so, since he was considered a prophet, a holy man. It seems her children were not his, 2.4-5.
v4-5: The name Jezreel was prophetic and meaningful, referring back to a massacre perpetrated by Jehu. The dynasty of Jehu lasted through Jeroboam's reign (2 Kings 10.30) to Zechariah (2 Kings 15.8).
Some 50 years after Jeroboam's death, Israel was defeated by Assyria. So this prophecy was quickly fulfilled, as the kingdom of Israel reached its end, and its bow broken.
v6-7: No mercy for Israel, but mercy for Judah; salvation is only by God's power, not by human strength, see 1 Sam 17.47; Zech 4.6. This was certainly fulfilled during Hezekiah's reign; in Is 37.33, the invading army was defeated, but not by military means.
v8-9: The third child, Lo-Ammi, for the relationship between God and Israel is broken. The sequence of names indicates growing severity in God’s judgment against His people.
v10-11: Yet Israel and Judah will be restored together, under "one leader," even Christ. Israel will be as numerous as the sand on the seashore; see Gen 13.16, where God originally gave this promise to Abraham. Such will be their repentance, that they will willingly appoint for themselves their leader. The relationship with God, broken as prophesised by Hosea, will be restored.