Hi rizello,
NSX Edge = centralized routing
on a medium-large environment normally we have NSX Edge clusters & NSX Edge Racks
traffic from/to outside NSX environment (e.g. internet) going to the edge cluster/racks first
gateway IP address is in the nsx edge gateway vm

NSX DLR = distributed routing
VM to VM communication do not need to traverse to edge cluster/rack
gateway IP addresses are distributed across esxi hosts which prepared for NSX

in a very small environment e.g. only 1 esxi hosts for example, having DLR does not make any differences.
but when you have multiple esxi hosts and VMs on different subnet/vxlan/logical switches are distributed across esxi hosts,
NSX DLR helps to route VMs between different logical switches optimizing east-west traffic
the picture is taken from the NSX design guide, more explanation is also available on the design guide
VMware® NSX for vSphere Network Virtualization Design Guide ver 3.0