It means for all eternity. It is a reaffirmation of the fact that God has always been, even before the beginning, a Trinity, each of Whose Members are due equal glory.
The actual Latin of the prayer is: Gloria Patri et Filio et Spiritui Sancto, sicut erat in principio et nunc et semper et in saecula saeculorum.
The part you are asking about is 'sicut erat in principio et nunc et semper et in saecula saeculorum'
"In principio" is the same phrasing that is used to start the Book of Genesis in Latin. In two simple words, here, we are reaffirming what we speak of in the Nicene Creed "I believe in one God, the Father Almighty, maker of heaven and earth... and in one Lord, Jesus Christ, the Only-Begotten Son of God, born of the Father before all ages... through Him all things were made... in the Holy Spirit, the Lord, the giver of life... Who together with the Father and the Son is worshipped and glorified."
"Et nunc et semper" has the meaning of "both now and always." Here, the first "et... et" can be translated as "both... and," even though the usual meaning of 'et' is simply 'and.' This is a reminder that we should, ever in the moment of the 'now' glorify God for all things and a reminder that God, throughout history, no matter how bad things get, will always be glorified.
The Latin word saeculum has a number of meanings, Lewis and Short listing "a race, generation, age, people of any time."
Saecula is the plural accuasative form because the preposition 'in' takes the accuasative form as its object when translated as 'into' or 'unto', which suggest motion, rather than just 'in' which suggests location. Saeculorum is the plural genitive.
So the more literal transalation of the prayer would be "Glory to the Father and to the Son and to the Holy Spirit, as it was in the beginning and, both now and always and unto the ages of ages."
The same prayer, in Greek, is "Doxa Patri kai Yio kai Agio Pnevmati kai nin kai aei kaei eis tous aionos ton aionon."
The Eastern form leaves out the "as it was in the beginning" but otherwise is translated literally in the same way as the translation I gave above.
Hope this helps.