Jesus simply means that the Father has shown Him to have His authority.
Has set His seal on translates the single Greek word σφραγίζω (sphragizō), which is related to the word σφραγίς (sphragis) - seal - used to describe the seal (or signet) that a king would put on a royal decree or writing*, e.g.
And they brought a stone, and put it on the mouth of the den; and the king sealed [ἐσφραγίσατο] it with his ring, and with the ring of his
nobles; that the case might not be altered with regard to Daniel
(Daniel 6:18 LXX)
Some paraphrase Bibles like the NIV have translated the phrase in John 6:27 His seal of approval.
Theophylact explains this phrase (translated from the Greek):
By the words, on Him God the Father has set His seal, He shows that
the power of working miracles, and the authority to save men, were
given to Him by the Father. For it was customary among men, when they
wished to send someone with authority, to give him a signet ring [σφραγὶς] as a
pledge of the power entrusted to him. Therefore, Christ was given to
us by the Father as a pledge of His authority, and He was sealed with
the Holy Spirit, who bore witness to Him at His baptism (PG 123:701)
*
The English word seal in the context of a mark or emblem indicating authority or authenticity has its origins in the Old French word seel, which meant a seal or stamp used to make an impression on wax or clay. The Old French word seel itself was derived from the Latin word sigillum which is a diminutive form of the noun signum, which meant a sign or mark (the Latin version of John 6:27 uses the verb signare). The word signum is also the origin of the English word sign, which has a similar meaning of indicating or representing something. The Saxon word was also derived from the Latin word left by the Romans to their ancestors. The modern German word for seal is Siegel. The Old English (Saxon) version of John 6:27 in the Lindesfarne Gospels is
Nelle ge wircað þa mete þe forweornað, ac þa mete þe standeð on ece
lif, þone mete mannes sunu eow sylð; for þæm þe God se Fæder his sette
his sele on hym.