Coronation ceremonies are full of symbolism. The associations of purple in royal ceremonial are obvious, and of course have Roman roots. Historically "púrpura" has two related meanings: (1) the precious and expensive dye, Tyrian purple (actually red rather than purple in the modern sense) extracted from a certain snail, and (2) cloth dyed with it, which is associated with emperors, monarchs and cardinals. It seems unlikely that the dye was offered here; it must surely be the cloth.

It need hardly be said that at a coronation purple (cloth) symbolises the power and dignity of the monarch.

Some other descriptions, worded differently, help us to understand what is happening here. We must, of course, concentrate specifically on medieval Navarra, and this is derived from the Navarrese fueros.

"Ofrecer" refers to an offering to God, in the sense of the offertories after the mass:

"noun, plural offertories.
1. (sometimes initial capital letter) the offering of the unconsecrated elements that is made to God by the celebrant in a Eucharistic service."
http://www.dictionary.com/browse/offertory

Here, of course, it has a special significance, as a symbol of royal submission to God and the concomitant suggestion that the monarch's power is derived from God.

Here are some other references:

"Hicieron lo que les aconsejaron, formaron y escrivieron los fueros: el primero fue establecer cómo se había de levantar rey y su juramento, ordenando que la noche antes vele en la Iglesia, y por la mañana asista al santo sacrificio de la Misa y reciba la Santa Eucharistía y ofrezca en el Altar Púrpura y de su Moneda; que puesto de pies sobre su Escudo le levanten los Ricoshombres clamando todos tres vezes: REAL, REAL, REAL, que derrame de su Moneda sobre las gentes y se ciña él mismo su espada, que es a semejança de cruz".
From Chavier, Fueros del Reyno de Navarra (1686), quoted in Alfredo Floristán, "El uso de la imagen como representación jurídica", in La historia imaginada: construcciones visuales del pasado en la Edad Moderna, 324, n. 21
https://books.google.es/books?id=ri_WrFHifCUC&pg=PT326#v=one...

(Note, by the way, that the offering includes both purple (cloth) and coins, and that subsequently the new monarch also scatters coins to the people; your "repartir su moneda" refers to the latter.)

"El ceremonial comprendía los siguientes pasos: vela de armas la noche anterior, asistencia a misa en la iglesia, ofrenda de púrpura y moneda, comunión, alzamiento sobre el escudo al grito REAL, REAL, REAL y lanzamiento de monedas sobre las gentes."
La Catedral de Pamplona, 1394–1994, 30
http://www.navarra.es/appsext/bnd/GN_Ficheros_PDF_Binadi.asp...

"Finalmente el obispo de Pamplona celebró una misa cantada, y al ofertorio ofreció el rey telas de púrpura y oro y sus monedas, según fuero, y comulgó de mano del obispo."
http://www.euskomedia.org/aunamendi/32620/15504

There are others, but these are enough, I think.

So it means an offering made, in the religious sense of an offering (to God), and what is offered is purple cloth and gold coins: power and wealth. The way it is phrased doesn't suggest that the monarch offers his own purple robe, but simply some purple cloth. "Purple", in English, commonly means purple cloth anyway, so the word "cloth" needn't necessarily be added for a specialist readership; you decide.

The offering is an element of many coronation ceremonies. Here is an interesting account of the coronation or our very own George IV in 1821:

"The Offering.— The King, attended by the two Bishops, his supporters, the Dean of Westminster, and the Noblemen bearing the Regalia and the four swords, passed to the Altar; where his Majesty uncovered, and kneeling upon the cushion, made his first offering of a pall or altar-cloth of gold."
A Brief Account of the Coronation of... George IV, 16
https://books.google.es/books?id=ZV8UAAAAQAAJ&pg=PA16