What does "proceeds" mean to Eastern Orthodox? The Eastern Orthodox Nicene Creed says:


  I believe in one God, Father Almighty, Creator of
  heaven and earth, and of all things visible and invisible.
  
  And in one Lord Jesus Christ, the only-begotten Son of
  God, begotten of the Father before all ages;
  Light of Light, true God of true God, begotten,
  not created, of one essence with the Father
  through Whom all things were made.
  Who for us men and for our salvation
  came down from heaven and was incarnate 
  of the Holy Spirit and the Virgin Mary and became man.
  He was crucified for us under Pontius Pilate, 
  and suffered and was buried;
  And He rose on the third day,
  according to the Scriptures.
  He ascended into heaven
  and is seated at the right hand of the Father;
  And He will come again with glory to judge the living
  and dead. His kingdom shall have no end.
  
  And in the Holy Spirit, the Lord, the Creator of life, 
  Who proceeds from the Father, Who together with the
  Father and the Son is worshipped and glorified, Who 
  spoke through the prophets.
  In one, holy, catholic, and apostolic Church.
  I confess one baptism for the forgiveness of sins.
  I look for the resurrection of the dead, 
  and the life of the age to come.
  Amen.


But what about God? It says God "proceeds" from God. According to Merriam-Webster Dictionary, proceed means:


  Full Definition of proceed
  intransitive verb
  
  1:  to come forth from a source :  issue 
  
  2 a:  to continue after a pause or interruption
  b:  to go on in an orderly regulated way
  
  3 a:  to begin and carry on an action, process, or movement
  b:  to be in the process of being accomplished 
  
  4:  to move along a course :  advance


According to Eastern Orthodox, what does "proceeds" mean?
Our Church teaches that these are the attributes of the persons of the Holy Trinity (fatherhood, begotten, procession),  and that we should not try to associate human concepts to them.
After all, what does "begotten" mean? Can it be humanly explained?
From my point of view, one can understand these just through revelation and not through ration.

[editing to reply to the first comment]
According to the dictionary, "born" means to "start to exist". But the Word has not start, there is no time notion within the Holy Trinity. According to the teaching of the Church, we cannot say that the Father was before the Son or the Spirit. There is no "before". This is what I mean that "born" should not be interpreted in human terms.
You can use "proceeds" to describe the relationship between the Father and the Holy Spirit and the fact that, somehow, there is a sort of movement (Gen 1,2 "the Spirit of God moved upon the face of the waters.") but we should not try to attach the human understanding in order to describe God. The Holy Trinity cannot be truly described in human terms. One can understand God inasmuch as one is in communion with God.