There are two kinds of sufferings in Buddhism: the suffering of Samsara and the suffering of exertion.
The suffering of Samsara, is famously defined as:
Birth is dukkha, aging is dukkha, death is dukkha; sorrow,
lamentation, pain, grief, and despair are dukkha; being together with the
unloved is dukkha; being apart from the loved is dukkha; unsatisfied thirst is dukkha.
Or to summarize, "this world sucks, get me outa here". As was pointed out by other respondents, this works as motivation for Spiritual Quest.
But there is a different kind of suffering in Buddhism, called the suffering of exertion. This happens whenever we go against, and through, our pathological habits; whenever we push ourselves beyond our comfort zone:
(in this translation the code-word for suffering is "stress")
Furthermore, the monk notices this: 'When I live according to my
pleasure, unskillful mental qualities increase in me & skillful
qualities decline. When I exert myself with stress & pain, though,
unskillful qualities decline in me & skillful qualities increase. Why
don't I exert myself with stress & pain?' So he exerts himself with
stress & pain, and while he is exerting himself with stress & pain,
unskillful qualities decline in him, & skillful qualities increase.
Then at a later time he would no longer exert himself with stress &
pain. Why is that? Because he has attained the goal for which he was
exerting himself with stress & pain. That is why, at a later time, he
would no longer exert himself with stress & pain.
Suppose a fletcher were to heat & warm an arrow shaft between two
flames, making it straight & pliable. Then at a later time he would no
longer heat & warm the shaft between two flames, making it straight &
pliable. Why is that? Because he has attained the goal for which he
was heating & warming the shaft. That is why at a later time he would
no longer heat & warm the shaft between two flames, making it straight
& pliable.
In the same way, the monk notices this: 'When I live according to my
pleasure, unskillful mental qualities increase in me & skillful
qualities decline. When I exert myself with stress & pain, though,
unskillful qualities decline in me & skillful qualities increase. Why
don't I exert myself with stress & pain?' So he exerts himself with
stress & pain, and while he is exerting himself with stress & pain,
unskillful qualities decline in him, & skillful qualities increase.
Then at a later time he would no longer exert himself with stress &
pain. Why is that? Because he has attained the goal for which he was
exerting himself with stress & pain. That is why, at a later time, he
would no longer exert himself with stress & pain.
This is how striving is fruitful, how exertion is fruitful.
As you can see, just like in some other religions, there is "positive and necessary suffering" in Buddhism. It is not pleasant to restrain one's impulses. It is not pleasant to meditate. It is not pleasant to go through one's fears and preconcepts. It is not pleasant to have one's ego die. But this suffering seems to be necessary in order to tame the mind, and, eventually, transcend all suffering forever, as explained in the surgeon parable:
It's as if a man were shot with an arrow thickly smeared with poison.
As a result of being shot with the arrow, he would feel fierce, sharp,
racking pains. His friends & companions, kinsmen & relatives would
provide him with a surgeon. The surgeon would cut around the opening
of the wound with a knife. As a result of the surgeon's cutting around
the opening of the wound with a knife, the man would feel fierce,
sharp, racking pains. The surgeon would probe for the arrow with a
probe. As a result of the surgeon's probing for the arrow with a
probe, the man would feel fierce, sharp, racking pains. The surgeon
would then pull out the arrow. As a result of the surgeon's pulling
out the arrow, the man would feel fierce, sharp, racking pains. The
surgeon would then apply a burning medicine to the mouth of the wound.
As a result of the surgeon's applying a burning medicine to the mouth
of the wound, the man would feel fierce, sharp, racking pains. But
then at a later time, when the wound had healed and was covered with
skin, he would be well & happy, free, master of himself, able to go
wherever he liked. The thought would occur to him, "Before, I was shot
with an arrow thickly smeared with poison. As a result of being shot
with the arrow, I felt fierce, sharp, racking pains. My friends &
companions, kinsmen & relatives provided me with a surgeon... The
surgeon cut around the opening of the wound with a knife... probed for
the arrow with a probe... pulled out the arrow... applied a burning
medicine to the mouth of the wound. As a result of his applying a
burning medicine to the mouth of the wound, I felt fierce, sharp,
racking pains. But now that the wound is healed and covered with skin,
I am well & happy, free, master of myself, able to go wherever I
like."