Boxer is a horse, and on a farm a horse has a lot of jobs to do. In the first chapter, we get a description of Boxer: "he was not of first-rate intelligence, but he was universally respected for his steadiness of character and tremendous powers of work" (p. 3). So Boxer isn't all that smart, but he works hard and has strong character traits that earn him respect from the other animals.
When the revolution begins, Boxer is one of the most faithful followers. He accepts the teachings of the pigs with dedication, and even throws his own hat into the fire to ensure that he goes naked like all animals should. Once the animals begin to be self-sufficient, Boxer is the hardest working one of all. "He had been a hard worker even in Jones's time, but now he seemed more like three horses than one; there were days when the entire work on the farm seemed to rest on his mighty shoulders," (p. 25). Of course, his motto for when times got tough became, "I will work harder." That was his solution to any problem: the idea that hard work would bring the desired result, and if he wasn't getting the desired result, he would simply work all that harder.
Just to add a little to that, Boxer is a workhorse or drafthorse. He is not the normal, thin-legged tall horse that cowboys ride; he's a farm horse. Slower than a normal horse, but much much bigger and stronger and with better stamina and temperament, they were used for ploughing and pulling heavy loads. Farms have got tractors now, so they don't need workhorses, but in the past horses like Boxer were very common.