A major theme in Bleach is the fact that Hollows, the restless and empty souls of the dead, cannot get a happy ending. From the very start, Hollows are presented as marauding monsters that devour innocent humans souls, it's the Soul Reapers' to slay these creatures. But later, it's revealed just how tragic a Hollow's afterlife can be.
During the Arrancar arc, Ichigo and his allies fight many Arrancar, powerful Hollows that have removed their masks. The most powerful among them are Sosuke Aizen's Espada, the ten most powerful Arrancar in Hueco Mundo, the dead desert. Among them is one Grimmjow Jaegerjaques, and his backstory is perfectly symbolic of what the Hollow life is really like.
The details of Grimmjow's human life are unknown, but at some point, he died and became a regular Hollow before going cannibal. He and other cannibal Hollows melded together to form a Gillian-class Menos Grande, but Grimmjow's personality was strong enough to override the others and take control of the entire being. Grimmjow the Gillian continued to eat other Hollows, and he morphed into the next class: an Adjuchas.
From there, he wandered the desert of Hueco Mundo, likely not bothering to visit the world of the living, eventually coming across a small team of smart Gillians. One of them, a certain D.Roy, challenged Grimmjow, only to get bitten. Impressed, the Gillians explained themselves and their quest to become Vasto Lorde-class Menos, and rule all of Hueco Mundo. They needed a strong leader to realize that dream, and they decided to accept Grimmjow as that king. Grimmjow took on the role of leader, and he doggedly pursued the dream of becoming a Vasto Lorde and ruling Hueco Mundo. He sneered at his fellows when their spirits broke, and Captain Sosuke Aizen found them sometime after that. All of them became Arrancar, and Grimmjow reluctantly accepted himself as a part of Aizen's plan. What he really wanted was the power to become a king, and Aizen had just given it to him. Or so he thought.
Grimmjow felt more empowered than ever, and he channeled this competitive drive into his desire to fight the strongest Soul Reapers he could find. Early in the Arrancar arc, another Espada named Ulquiorra scouted Karakura Town to assess Ichigo Kurosaki's strength, finding a powerful but unstable warrior with vast potential for growth. Eager to prove his worth, Grimmjow traveled via a Garganta to assassinate Ichigo, and after their first clash, a bitter rivalry was born.
Grimmjow returned later to fight Ichigo again, this time to a stalemate. Later, as Ichigo and his friends trekked to Hueco Mundo to storm Las Noches (Aizen's palace) and rescue Orihime, Grimmjow took the drastic step of turning on the other Arrancar and rescuing Orihime himself so he could make sure that his final battle with Ichigo would be the best yet. Orihime healed a fatally wounded Ichigo, and Grimmjow got his final duel. And lost.
Grimmjow wanted so badly to become "the king," and that meant defeating Ichigo to pave the way to ultimate power. Although Ichigo wasn't an expert on Hollows, he knew that Grimmjow's quest was totally in vain, because it entailed Grimmjow killing everyone around him until no one was left, leaving Grimmjow the king of absolutely nothing. Indeed, a Hollow's life is one of pain, fear, hunger and desperation, since there is no salvation for Hollow-kind, even if they really do become the king of Hueco Mundo, like Barragan once did.
Grimmjow was forced to accept this bitter truth, and by the time he appeared again in the Thousand-Year Blood War arc, he was a lone wanderer who was desperate for something meaningful in his life. He reluctantly aided Ichigo against the Sternritter, since he couldn't stand the idea of his #1 rival getting killed by any other party. This came to nothing, though, and presumably, Grimmjow returned to wandering aimlessly after Ichigo's triumph over the Wandenreich. This was the hard truth that Hollows and Arrancar had to accept, and Grimmjow did too, though he'd never admit it, possibly not even to himself. He's too proud as the would-be king.