1.  The Pentangle in the Text
2.  Is the Pentangle a Talisman?
3. The Poet's Own Allegory of the Pentangle
1.  The Pentangle in the Text: SGGK is the only Arthurian narrative in which Gawain carries a "pentangle" on his shield. Usually he has a golden eagle, a lion, or a gryphon. SGGK is the first text to use the word "pentangle" in English (see Oxford English Dictionary, pentangle). A pentangle is a pentagram, a five-pointed star, and this raises the question of whether the pentangle has the magical associations that the pentagram has today.
First, what does the pentangle look like? This sketch shows Gawain in the armor mentioned in lines 566-618. Here the pentangle is on his chest (lines 636-37). We must imagine how it looks on the shield, which his squire holds so that the image of Mary on the inside is facing us. Source: Helmut Nickel, "About Arthurian Armings, For War and For Love," Arthuriana 5.4 (1995), 3-21, at 12.
Next, what does the text say about the pentangle? Line 625 says that the pentangle originated with the Biblical figure Solomon, king of Israel after David: "sign by Solomon sagely devised." For the Biblical account of Solomon, see 1 Kings 1-11. Archeologists have found five-pointed stars in earthenware near Jerusalem. Source:  J. Schouten, The Pentagram as a Medical Symbol (Amsterdam, 1958), p. 22.

Whatever the source of the poet's stsatement that Solomon invented the pentangle, that source is now unknown.

The poet also calls the pentangle a "token of truth" (Middle English trawthe ‘faithfulness’) in line 626, which points to the theme of faithfulness in SGGK: Gawain is tested for his faithfulness to all of his promises--to the Green Knight in the so-called "beheading game" and to Bertilak in the so-called "exchange of winnings."

The poet also calls the pentangle an "endless knot" (line 630), which sounds like a folk or popular name for the pentangle, but as with the attribution to Solomon, there is no evidence for this outside the text of SGGK.

2.  Is the Pentangle a Talisman? It is tempting to think of the pentangle as a pentagram, and pentagrams are part of Northern European folklore. In German, the pentagram is called a Drudenfuss (earlier trutenvuoz). The term refers not to the footprint of a Druid but to the footprint of a Drude / trute ‘witch’ or a ghost producing nightmares. You would draw a pentagram on the sill to prevent a trute from entering the house/room--perhaps to convey the message "you cannot enter here because one of your kind is already inside" (Otfried Lieberknecht on Medtextl 4 July 96)
Here is an illustration of a pentagram used as a Drudenfuss. Source:  J. Schouten, The Pentagram as a Medical Symbol (Amsterdam, 1958), p. 31. Jim Marchand (Medtextl 5 July 96) adds that the Drudenfuss was also put on cradles, and that Goethe has Faust draw one in Faust, but badly, so that Mephisto can come in but not out. Marchand compares the Drudenfuss to hex signs on Pennsylvania Dutch barns. "On the impenetrability of the druidic limits" [says Marchand, just a few lines after disavowing Druid’s foot as folk-etymology] "note the concept of the airbe druad ‘druid’s hedge’ around an army which could not be crossed. In late medieval England, people would recite charms and spells that invoked the power of the holy objects represented on Gawain's shield.  As such, the pentangle would be an example of apotropaic (warding off evil) magic, and when Gawain enterns Bercilak’s castle and then takes off his shield, he would be laying himself open to magic. Indeed, he succumbs to the lady’s temptation and accepts the supposedly magic green girdle, although she uses no magic on him, while he is away from his pentangle.

The problem with this interpretation of the pentangle is the lack of evidence for the magical significance of pentagrams in late-medieval England and the lack of tectual evidence in SGGK itself that the pentangle on Gawain's shield has magical properties. Like the green girdle that the Lady offers to Gawain later on, it does not protect GAwain from the Green Knight's axe: the Green Knight is able to cut Gawain on the neck.

3. The Poet's Own Allegory of the Pentangle

The poet spells out the significance of the five points on the pentangle for the reader in lines 640-55. Here, he associates each of the five points of the pentangle with a set of five virtues that define Gawain. :

First he was found faultless in his five senses,                        640
And next he never failed in his five fingers,
And all his belief on the earth was in the five wounds
That Christ caught on the cross, as the Creed tells.
And wherever in melee that this man was put,
His whole thought was about this, through all other things:      645
That all his force he received from the five joys
That the gracious queen of heaven had in her child.
Inspired by this [ at this cause ], the knight fittingly had
Her image depicted inside of his shield,
So when he looked at it his boldness never failed.                 650
The fifth of the fives that I find in the man
Were franchise and fellowship beyond everything,
Cleanness and his courtesy that never went wrong,
And pity, surpassing all virtues.

[“Creed” = Apostle's Creed, an ancient Christian affirmation of basic beliefs; The Five Joys of Mary are the Annunciation, Nativity, Resurrection, Ascension and Assumption. With the five wounds of Christ, they were subjects of devotion in late medieval popular culture; “franchise” = in one sense, aristocractic privilege, in another, the generosity -- also called “freedom” -- made possible by aristocratic wealth and rank; “fellowship” = usually translated as “brotherly love” or the equivalent. Both of these words describe both extrinsic and intrinsic qualities. Gawain has franchise by virtue of his social position, but he practices franchise through his generosity to others. Gawan has fellowship by virtue of his membership in a court, but he practices fellowship through his kindness to his fellow nobles. The blurring of internal and external qualities here -- note that they are said to be both fastened to him and fixed in him in lines 655-6 -- parallels Gawain's beliefs later that the Green Knight has “stuck” his promise onto him (line 2194) and that his failure at the Green Chapel is something simultaneously external and internal.]

One way of reading these virtues is that they present a construction of an ideal knight in physical, religious, and social terms:

1. Five senses: sight, hearing, touch, smell, taste: natural intelligence.
2. Five fingers: natural strength.
3. (Faith in) the 5 wounds of Christ: 2 hands, 2 feet, 1 side (see lines 626, 632).
4. (Force founded in) the 5 joys of Mary: Annunciation, Nativity, Resurrection, Ascension, Assumption.
5. Five miscellaneous virtues: in ME fraunchyse, felawschyp, clannes, cortaysye, pité, which I translate as literally. Note that these are social, not religious virtues, and that Gawain's religious faith is defined in terms of popular theology--as befits a knight rather than a priest. These twenty-five virtues would thus add up to a knight who is physically strong, who is devoted particularly to the Virgin Mary and to Christ--whose wounds are an apt focus for a knight whose purpose in life is to bleed for his lord as Christ bled for His Lord--and who manifests the ideals of courtly society.