How do I know it's a "she" and not a "he?" The male has a patch of red on the back of his head. This one didn't have that feature, so it's a female.
This is the Hairy Woodpecker (Picoides villosus). It's very similar in many ways to the Downy Woodpecker (Picoides pubescens). How can you tell them apart? Most people say that the easiest way to tell them apart is that the hairy is larger than the downy. That's useful to know, but it's not always helpful if you don't have both of them in front of you to compare. The downy is about 6-7 inches (15-18 cm) long, whereas the hairy is about 9-9.5 inches (22-24 cm) long. At a distance, it can be hard to say.
My preferred method of telling them apart is beak length, which you can see fairly well even by eye, and very well with binoculars.
The smaller downy woodpecker has a smaller beak that is about a quarter of the total distance from the tip of the beak to the back of the head. The larger hairy woodpecker, as I've tried to show in the picture below, has a beak that is at least a third and sometimes almost half of the distance from the tip of the beak to the back of the head. That's my way of knowing which is which.
It was lovely to have her visit the yard. She went all the way up the laundry post and flew away once she got to the top. I hope I'll see her again!