Without knowing the full extent of what you have studied in class, I can offer an explanation of Boethius’s view on happiness. In fact, his position is fairly simple: Boethius believed that true happiness exists only in God.
In his time, Boethius saw many people attempting to gain happiness by seeking to accumulate material goods. Some modern examples of this might be a bigger paycheck, a nicer car, a house, or specific high-end item like a flat-screen TV. It was confusing to see so many people who behaved unkindly or selfishly, acquiring so many of these things. It seemed like they were being rewarded, even though they were living in a way that was opposite to what God asked for.
Boethius addressed this confusion by proposing that all those things—any material goods at all—were in fact contrary to happiness. Things do not make a person happy. Instead, the only way to be truly happy is to love God and seek to be as much like Him as possible. God does not make the way easy, as evidenced by Jesus's suffering and death on the cross. Instead, the key to happiness is to accept life as it is, love God, and understand that God does what is best for us, not what it easiest or most comfortable.
Therefore, for Boethius, happiness is complete submission to God and whatever life brings, always keeping God in the forefront of one’s thinking about life. God, he believed, was the only true source of happiness there is.