All the people on the trip to Canterbury were pilgrims, there is no one character called "pilgrim". The parson, however, is one of the pilgrims in the group. The parson was one of the few members of the clergy that Chaucer liked and so he gave the parson favorable traits. The General Prologue doesn't give a physical description of the parson, but based on the fact that Chaucer gives other favorable characters such as the Oxford scholar traits such as thinness, it's safe to assume the parson is thin. Plumpness, such as was found in the character description of the Prioress and the Friar, were equated wtih undesireable characters who took advantage of their position and didn't share with the poor. Chaucer tells us that the parson tended to his flock more than himself, so it is reasonable to conclude the parson was not only thin, but probably appeared to be very poor. He was most likely dressed in very simple, humble attire. Also, since he walked, as Chaucer tells the reader in the General Prologue, to visit any of his parishoners who were ill or grieving, he probably is not only lean, but physically fit. The parson's tale and prologue do nothing to expand on a physical description. But since his tale and his description in the GP both note that he is a somber and devout man, he probably wasn't a man to smile a great deal.
You might have meant to ask about the parson and the plowman, as they are brothers. I can add some input on the previous answer about the plowman.
As his name implies, the plowman is a manual laborer whose job was to literally haul and spread animal waste. He is described in the prologue as such:
With him [the parson] there was a plowman, was his brother
That many a load of dung, and many another
Had scattered, for a good true toiler, he,
Living in peace and perfect charity.
The speaker notes that despite his rather smelly, dirty and generally low-level job, the plowman lives a happy life and works to serve others.
His appearance, like his brother, would be thin, and his clothing would be simple, dirty, and perhaps torn. He is not a wealthy man, so his face and hair would not be groomed. However, one might imagine the plowman to smile and to engage in some friendly talk when he is not at work. He seems to be content with his life, however meager his earnings may be.
He is described as riding on a mare, which is a bit odd for a lowly servant. One may assume that the mare was provided to both the parson and the plowman by the church.