A. "When forty winters shall besiege thy brow,"
B. "And dig deep trenches in thy beauty's field,"
In these first lines, Shakespeare uses "forty winters" to call up the pain and cold of winter, just as if you were aging. Forty winters also means forty years. "shall besiege thy brow" is referring to back in the day, when someone would dig a trench and wait, attacking continuously over a period of time (lay siege). So he is comparing this youths brow, or forehead, to the wall of a castle being attacked over a period by time and old age.
If you dig a trench in a field it will not look the same, even if you fill the dirt back in it will never look like it did once before. Time, age, has dug trenches into "beauty's field" the beauty of youth, and that is something that will never return.
Sorry this answer is late, but I'll put it here for anyone still looking, or if anyone needs confirmation, since the other answer here is correct.