The Greek words translated as "glorify" and "glory" are from the same Greek root, but the translation of that root as "glory" is misleading. The English was chosen more to praise than to translate Jesus’s words. The praise aspect of these words is not central to their meaning.
A more accurate translation of “glorify” and “glory” in today's English would be "recognize" and "recognition." However, what is recognized is a person's "reputation." "Recognizing" someone also means spreading their reputation, as we might say, "publicizing" or "promoting." In Greek, these words can be positive or negative, depending on whether the reputation is positive or negative, but they are used, especially by Jesus, primarily in the positive sense.
The Greek
The Greek verb is doxazo (δόξα), which means holding something or someone in your mind or imagination. Its secondary meaning is to "extol" or "magnify," which is where the meaning of "glorify" as in "praise" arises. The word gets its meaning of "magnify" from our tendency to imagine things as bigger than they are. In the Latin Vulgate, the Greek verb was translated as clarifico, which means "to make illustrious or famous." Interestingly, this Latin word is also the source of the English, "to clarify," which goes back to the primary meaning of the Greek, having a clear image in your mind.
The noun is doxa, (δόξῃ), which originally meant "expectation" and "opinion." It came to mean "reputation," especially "good repute", "honor", and, rarely, "ill repute." It came to mean "glory" and "magnificence" in external appearance through Christian writing after the Gospels.
English Translation
In translating Jesus’s words, it always works best if we can find a verb and noun from a common root in English that can translate a Greek noun and verb from the same root like “glory” and “glorify.” “To recognize” works for doxazo, and "recognition" works for doxa. This idea of "recognition" captures the mental imaging part of the concept and the idea of honoring. By giving people recognition, we make them better known and more broadly respected. By giving someone recognition, we make them better known and more broadly respected. This is the idea of being a "recognized authority."
To maintain the connection between the noun and the verb, “recognize” and “recognition” should be used to preserve the connection, especially when both appear in the same verse or in nearby verses. While "reputation" is technically more accurate, "recognition" also has a sense of praise in English. We give people recognition when we give them awards, for example. Since Jesus often uses this word only in the sense of a shining reputation, so “prominence” may work best in some contexts.
Since the verb form also has the sense of spreading someone's good reputation, "publicize," "promote," and "proclaim" also capture some aspects of its meaning. The role of Jesus’s apostles as “the ones sent” (the meaning of the Greek word for “apostle”) was one of promoting and publicizing Jesus and his teaching. In Jesus's era, the process was almost entirely word-of-mouth, more like the peer-to-peer communication on the Internet today. People share information with others because it is interesting.
Today's advertising is the most common form of "glorification." Advertising is used to create images in our minds, making people and things more illustrious and famous. We could use "advertise" or "promote" in the place of "glorify" in today's translations of Christ's worsd, but many would certainly think of that as disrespectful.
Recognition and “Name”
A concept closely related to the idea of "glory" or “reputation” is the word translated as "name" (onoma). Someone's name represented their reputation. It was how they were recognized. A person's name was also a sign of their authority and responsibility. "Recognizing a name" means recognizing someone's authority. When someone "acted in the name of another," they were recognized as representing them. See this article for more about the Greek concept of "name."
Jesus describes his role as "to glorify [God's] name" (John 17:6). This promoting God's name and making it famous, is his goal (John 17:4). However, this is a reciprocal process. The Father must make Jesus famous so Jesus can make the Father better known (John 17:1). In today's terms, we might say Jesus’s job was marketing God's name. Jesus’s life was designed to allow his message to "go viral."
Conclusion
The Father cannot be seen directly. Jesus describes the Father as hidden more than once (Matthew 6:4, Matthew 6:18, John 6:46, etc.). The Divine can only be imagined or recognized in His reflection in others, primarily in Jesus. Our recognition doesn’t magnify him, make the Divine any greater or better. It only makes his image clearer in our minds.