What does it mean that God is omnipresent?

The word omnipresent is just a big word meaning present everywhere.  It does not mean everywhere present (to say that God is in the trees, rocks, etc.) but that God’s presence is everywhere.  There is nowhere we can go at all to escape God’s presence (Psalm 139:7-9).  God’s presence is felt everywhere once a person is saved and that person has the Holy Spirit with them, as does all believers in Christ (John 14:16-17).  Remember that wherever you go and whatever you do that God is always going to be right there with you and if you are His child He will never leave you nor forsake (abandon) you (Hebrews 13:5).