가져가다(ga-jyeo-ga-da, gajyeogada)
Means to take something or someone from the current location to another place.
When to use
Movement from starting point, Moving something elsewhere, Away from speaker's location
The nuance
Used when moving something away from the speaker's current location or point of reference to another place.
가져오다(ga-jyeo-o-da, gajyeooda)
Means to bring something or someone from another place to the current location.
When to use
Movement toward destination, From elsewhere to current place, Closer to speaker's location
The nuance
Used when bringing something or someone from another place to the speaker's current location or reference point.