Answer: When the Bible speaks of glory it generally refers to how a being or a person appears. Scripture records several people, including groups, seeing and experiencing the glory of God. Most of these examples occur in the Old Testament.
Israelites got to witness the Eternal's glory when he personally spoke to them, from Mount Sinai, in order to give them the Ten Commandments (Exodus 20). After they agreed to keep his law, He arranged for a covenant meal between him, Moses, Aaron, Aaron's two sons and seventy of Israel's elders (Exodus 24). It was at this meal that God's glory was seen by these seventy-four men.
The average Israelite was also able to view the majesty of God not only on Sinai but later at the tabernacle in the wilderness (Exodus 24:16, 40:35, Leviticus 9:23, Numbers 16:42).
Moses made his own unique request to view the glory of God. He asked if he could view what the Lord actually looked like up close. His requested was granted but he was only able to view his "back parts" as he walked by (Exodus 33:18 - 23).
God had to make another copy of his commandments after the first one was broken due to the people's sin of idolatry (Exodus 32:19). Moses' face, after spending forty days on the mount receiving it, was luminous from the glory he saw. His face shone so brightly after coming down from Sinai that they Israelites could not look at him (Exodus 34:29 - 35, 2Corinthians 3:7)! His shining face was so bright that it required him to wear a vail over his face any time he spoke to the people.
Sharing his holiness
In 1Corinthians 15 the Apostle Paul states that resurrected Christians will bear the image of (appear like) our spiritual elder brother Jesus Christ. This means that someday those who are converted will be made to shine with glory given them as a reward from God!
As is the one made of dust (Adam), so also are all those who are made of dust; and as is the heavenly one (Jesus Christ), so also are all those who are heavenly. And as we have borne the image of the one made of dust, we shall also bear the image of the heavenly One (1Corinthians 15:48 - 49, HBFV throughout).
The prophet Daniel confirms this encouraging promise of receiving some of God's glory when he states the following.
And they who are wise shall shine as the brightness of the firmament [heavens], and they who turn many to righteousness (by preaching the gospel, etc.) shall shine (with glory!) as the stars forever and ever (Daniel 12:2 - 3).