The northern kingdom of Israel, soon after it established its independence from Judah, was evidently quite tolerant of the worship of several gods. While there were holy places to worship God (notably at Shechem), people began building altars and pillars to worship other gods, the most famous of which was Baal. Hosea likens this behavior to a woman who cheats on her husband. God responds as a man would to a cheating woman -- distrusting, separating from, and seeking a just settlement (though justice her takes the form of punishment, rather than a financial agreement).
Ironically, Israel has begun to sense that there may be trouble ahead, as foreign armies threaten to invade. So they have tried to curry favor with the gods by worshiping more, including by praying and sacrificing more to the true God. However, this behavior only seems to further prove the problem that Israel cannot and will not trust in God alone. So they cannot stop the coming defeat. However, God still loves this people, and promises a day when the loving relationship will be reconciled.
Note: One of the challenges of reading the prophets is understanding the use of the term "Israel." Sometimes it refers to the northern kingdom of Israel; sometimes it refers to all of the descendants of Jacob (Israel). This double-usage occurs throughout the prophets. In Hosea, "Israel" usually refers to the northern kingdom, but sometimes it seems to refer to all those of Jewish heritage in both the northern and southern kingdoms.
