OSPF ABR ( Area Border Router ) is the router that non backbone area routers use it as exit from their area. In the OSPF RFC it is stated that if one router has two interfaces on the two area it can be considered as an ABR.
But in the implementation , in order to have an ABR , router needs to have at least one interface is connected to area 0 which is backbone area.
In the figure, R3 is the backbone router but not an ABR since it has only connection to the Area 0. In order to be an ABR , router needs to have one interface in Area 0 and other at least one interface in different area.
R2 and R6 has a connection to both Area1 and Area 0 thus they are ABR. Also R4 is an ABR since it has a connection to both Area 0 and Area 2.
ABR aggregates topology information from one area to another area. What does it mean ?
In the figure although R3 seems only one router in the backbone area, let’s consider we have other routers in the area 0 as well. Their connections to each other and metric informations is not sent to other areas by the ABR.
Instead , ABR only sends the reachability information. The routers in different areas only know that they can reach each other but with the information provided by the ABRs.
Thats why , if you design multi area OSPF network , you can’t have end to end visibility. A router can have topology information about its own area only,