Grimmjow did not understand the concept of love. Actually, it would be more accurate to say that he did not believe in love.
Yet he finds himself watching Ichigo, hour after hour, day after day. Disguising his reiatsu, he shadows the boy as Ichigo goes from home from school, observing him as he defeats hollows, watching him when he's asleep, a trace of his trademark scowl still on his face.
He notes the passion with which Ichigo protects those who are important to him. He discovers that Ichigo possesses a potentially fatal, inherently forgiving streak. He learns of Ichigo's inherent stubbornness to accept that there is anything that he cannot do, and finds that Ichigo has a surprisingly kind heart which he tries to cover with a tough, no-nonsense exterior.
No, Grimmjow doesn't believe in love. But recently, as he gazes down at the security screens in Hueco Mundo, at the orange-haired idiot running around with a green-haired child perched on his shoulders, he wonders if he could learn.