Knights in the Middle Ages wore a coat of arms to distinguish themselves from one another in battle.  Within a given family individuals would have their own coats of arms, separate from each other and sometimes blending with another family, depending on the circumstances of marriage.  A family would also have crests and seals, which might or might not be the same as the coats of arms.  All are referred to as heraldic devices.

“Generally the language of heraldry suggests its warlike origin. The term Coat of arms is derived from the surcoat worn over the armor to keep off the rays of the sun. It was a waistcoat-like garment, on which the heraldic design was depicted. The knight wore the arms shown on the surcoat on his shield, the trappings of his horse, and his lance pennon. In addition, he might have painted on his helmet what was called his crest. Not all knights chose a crest. The motto is not an integral part of the coat of arms, and may be changed at the will of the user.”  http://www.familynamesonline.com/coahistory.html

“The date and manner of the origin of coats of arms, often called family crests, has been a matter of much speculation. There is no evidence of coats of arms being present at the Battle of Hastings in 1066, nor were family crests apparent by the beginning of the twelfth century. However, in the 13th century, coats of arms were used throughout Europe and the whole ‘science’ of heraldry – its rules and terms – had been established. During this time the Crusades undoubtedly helped spread the use of coats of arms.

Various suggestions have been put forward regarding the origin of coats of arms, for example: shields, banners, tabards and possibly the use of seals. Probably, once a design had been adapted, it would have been put to many personal items at the same time. To qualify as a coat of arms, a design must be capable of being depicted on a shield, but the name ‘coat of arms’ is derived from the linen tabard which was worn over the armour and upon which the design was shown.”

http://searchwarp.com/swa20112.htm

The coat of arms for Gwynedd was this:

The personal coat of arms for Llywelyn ap Gruffydd was this:

This was clearly derived from the coat of arms of Gruffydd ap Cynan, father of Owain Gwynedd, who was  himself the grandfather of Llywelyn Fawr, Llywelyn ap Gruffydd’s grandfather:

And this is the coat of arms of  Dafydd ap Gruffydd, whom Edward I hanged, drew, and quartered in 1283 (or had hung, drawn and quartered, I suppose, since he didn’t do it himself :):

Wikipedia has a great list of other heraldic devices for the rest of Wales:

http://en.wikipedia.org/wiki/Welsh_heraldry

For translations of Welsh Latin mottos, and more information in general about Welsh mottos, see:  http://www.doomchicken.net/~ursula/sca/motto/welshmottoes.html

“English, Welsh, French, and Latin mottoes were all used in sixteenth- and seventeenth-century Wales. The following table shows their relative frequencies:

(A few mottoes were bilingual, and are therefore counted twice; one motto, “Odexi du parmer,” has been omitted from the analysis because its language could not be identified.)

Latin mottoes predominate. This reflects a widespread literacy in Latin; it may also indicate that the more overtly intellectual imprese mottoes influenced heraldic motto choices. British war-cries were often in French; sixteenth- and seventeenth-century men and women who displayed French mottoes could have inherited them from French-speaking ancestors, or they might have been displaying their knowledge of a foreign language. The bearers of Welsh and English mottoes, on the other hand, presumably spoke these languages at home.”

Sources for images:  http://commons.wikimedia.org/wiki/File:Coat_of_arms_of_Prince_Dafydd_ap_Gruffydd.svg

http://commons.wikimedia.org/wiki/File:Personal_arms_of_Llywelyn_ap_Gruffudd.svg

http://en.wikipedia.org/wiki/File:Coat_of_arms_of_Wales.svg

http://en.wikipedia.org/wiki/Welsh_heraldry