He discusses the following:
"...in man reflection comes in... develops his susceptibility to happiness and misery to such a degree that, at one moment the man is brought in an instant to a state of delight that may even prove fatal, at another to the depths of despair and suicide." (On the Sources of Suffering)
So, the first source of suffering discussed is one's capacity for reflection, which might produce things like disappointment and boredom. Broadly speaking it underlines all other sources of suffering.
"...in order to increase his pleasures, man has intentionally added to the number and pressure of his needs, which in their original state were not much more difficult to satisfy than those of the brute. Hence luxury in all its forms; delicate food, the use of tobacco and opium, spirituous liquors, fine clothes, and the thousand and one things than he considers necessary to his existence." (ibid.)
So, the second source discussed is luxuries, and all deliberate attempts to increase one's pleasure.
"And above and beyond all this... ambition and the feeling of honor and shame... what he thinks about the opinion other people have of him. Taking a thousand forms, often very strange ones, this becomes the goal of almost all the efforts he makes that are not rooted in physical pleasure or pain." (ibid.)
This in addition to things like romantic love is the third source he discussed.
Now, the quotation you mentioned is a rhetorical point about the abundance and intensity of suffering in the world. So much so, that basically if suffering isn't the point of life, then we are instantly failures, because of how much (at least to Schopenhauer) we're consumed by suffering. For him, it blots out every other positive thing in life.
If this still sounds confusing, let me try to simplify further:
"Unless suffering is the direct and immediate object of life..."
Translation: If suffering isn't the point of living...
"...our existence must entirely fail of its aim."
Translation: ...then what can we possibly do to justify how much of it exists? (Schopenhauer implies in this quote that nothing can justify it.)