In the early medival period, gift giving between kings was common and political. A gift from a greater power to a lesser one (as here) showed that relations between the two states were cordial.

Gifts also sent more particular messages. In Charlemagne's day, most western Europeans considered the Avars to be identical to Huns who terrorized the Western Roman Empire in its dying days. When Charlemagne sacked the hring of the Avars, he both gained a great deal of plunder and achieved an immensely symbolic victory over a foe his contemporaries blamed for for the fall of Rome. Little wonder, then, that Charlemagne gave gifts from the Avar horde to everyone who was anyone. Offa received a bit, as did Offa's bishops. So too did the Anglo-Saxon king of Northumbria. And the Northumbrian bishops. And, of course, the pope in Rome. And pretty well every count, bishop, and abbot between Northumbria and Rome. The Avar plunder was a sign of Charlemagne's military prowess. His free distribution of it a sign of his generosity. The broad advertisement of both of these virtues paved the way for his transition from Frankish king to Roman emperor in 800.

So, in context, it would have been more remarkable if Charlemagne hadn't given something to Offa. Remarkable, but necessarily unexpected. For, in the early 790's, the two kings hadn't gotten along well. The problem was twofold. First, Charlemagne had asked for Offa's daughter to be married to his son. Offa had responded by asking for Charlemagne's daughter to marry his son. Charlemagne was incensed by this: as a general matter of statecraft, Charlemagne was extremely reluctant to let his daughters marry anyone, yet alone the prince of a two-bit state in dreary old England. Unkind words were exchanged. Both sides issued trade sanctions. Second, exiles from Anglo-Saxon states tended to congregate at Charlemagne's court, much as in antiquity disgraced Greek politicians often wound up in the court of the Great King of Persia. Some of these exiles, such as the unfortunately named Prince Ecgberht, had claims to land Offa possessed or desired, and were therefore a threat to him. Their continued existence at Charlemagne's court was a source of tension.

The gifts of 796 and the (entirely conventional) fraternal language of the enclosed letter are therefore a sign of a rapprochement between Charlemagne and Offa. It is a rapprochement largely on Charlemagne's terms. There can be no reciprocal gift to match the glory of Avar treasure. As a gift, it reinforces the vast gulf between the two states that also prevents reciprocal royal marriages. Charlemagne's letter goes on to touch upon the case yet another Mercian exile who washed up on the continent. The tone is polite, but firm. The exile is a priest, so rather than return him to Mercia, Charlemagne has sent him on to Rome to be judged by the pope.

Charlemagne may not have ruled in England, but he did meddle. He received exiles, asked English bishops to attend his synods, and interceded in domestic matters. When he didn't get his way, he imposed sanctions. The letter and gifts of 796 are part of this broader approach to England.

I consulted Joanna Story's "Charlemagne and the Anglo-Saxons" in Charlemagne: Empire and Society (2005) for the details about Mercian/Frankish relations. It might provide good further reading for those interested in the topic.