I was looking at this photo and the shadows on face caught my eyes:
The stripes on shirt and hair are normal. It can be the shirt's pattern. And about the hair, it's to differeniate layers of hair.
But why are the shadows on face also made by stripes?
As you can see, my question is also tagged with style-identification, so I want to know the name of this style as well.
But more important I want to know the significance of the use of stripes to make shadows.
If you follow the link from the Wikipedia page, you get to the portrait's page at the National Portrait Gallery. That tells you it's a woodcut. It's probably wrong (see Joachim's answer, and the piece is more likely to be an engraving, but the reasoning below applies to both.
Like most forms of printmaking, woodcuts can only print ink or no ink. That means that to get anything that's not pure black or white you need some form of halftoning. So the question becomes one of what how do you achieve halftoning by carving wood. Lines are both easier to carve and more robust than trying to leave behind a stipple pattern, and so they're a logical choice to get intermediate shades.
Stripes, like other forms of shading, convey more than just simple brightness. Look at how they're used to show the curvature of the face and the curls in the hair. Also look at how the lines taper approaching a highlight
I'm going to be polemical and say that, even though the National Gallery categorises it as a woodcut, it is more likely a line engraving.
It is not easy to create fine, smooth, and steady lines in wood. Wood has grain, and specific directions it wants to guide the gouge into.
A woodcut is usually characterized by lines of uneven and often irregular width; hatching that, when curved, tries to follow along the natural grain of the wood; curves that are only slight, or suffer imprecision (sudden changes in width where part of the wood chipped away); variations between darker and lighter patches, when, for darker parts of a drawing, the surface layer of the wood would be mostly left intact; crossing lines will generally show signs of abrasion; and similar telltale signs.
The print you show consists completely of lines—even the dark hair, the lines of which in a woodcut would have been engraved into the top layer, consist entirely of lines. Very smooth lines. The lines in the hair and especially around the chin are very fine (this illustration is around 8 cm high), and perfectly curved.
The very clean illustration screams intaglio printing, not relief printing.
This is a woodcut of James Hind from 1652, that is 2 years after the illustration you posted was made:
I think the differences in the technique used are apparent—note especially the boots.
Here is another etching of James Hind, just to hammer it home (albeit this is from 1799):
Here you can also see the darkest patch is actually hatched.
The possible cause for the probable misinformation on the page ChrisH links to in their answer, is that it categorizes the entire piece of paper (the dimensions verify this assessment), which, as can clearly be seen, is the illustration you refer to attached to a piece of printed paper: the illustration and the lettering are separate processes. I'm not sure why it is categorized as a woodcut, though. Perhaps the lettering was done using woodcut, but this is unlikely.
Like the Flemish painter Anthony Van Dyck heavily influenced the baroque in England, which came up around the time the image was made, so the German Hans Holbein Jr. influenced the English Renaissance prevalent during the Tudor period. This period ended with Elizabeth I, only a few decades before the illustration in question was made.
But its style seems archaic for the time (it, for example, really stands out in this list of portraits made around the same time). It is a small line engraving, perhaps intended to be more decorative than descriptive, and could have been part of a larger collection of portraits of criminals; in any case, it is rather crude as a portrait of an individual. It is very rigid, and prototypical. It also seems very traditional, almost medieval in style, and is certainly not baroque.
It is therefore difficult to pinpoint the style of this image, especially because it was likely never intended as "art", and artistic and personal preferences did not play a part in the creation process.
The clothing worn by the sitter is slightly more elaborate than what Shakespeare is wearing in this painting, and I would say that, at least, is contemporary.
The type of image, in which the face or bust of a specific person is depicted, is common for biographical texts, or as part of or opposing the title page of iconic books or editions. Hopefully that can be a lead.
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