Suppose you have a topology R1---R2 and R2 advertises 2.2.2.2 to R1 via RIP.
By default RIP would set the metric as 1 (1 hop)
With Offset list you can change the metric that is advertised
R1
interface FastEthernet0/0
ip address 10.10.10.1 255.255.255.0
router rip
version 2
network 10.0.0.0
no auto-summary
R2
interface FastEthernet0/0
ip address 10.10.10.2 255.255.255.0
router rip
version 2
network 2.0.0.0
network 10.0.0.0
no auto-summary
The route on R1 shows the metric as 1
R0#sh ip route
2.0.0.0/24 is subnetted, 1 subnets
R 2.2.2.0 [120/1] via 10.10.10.2, 00:00:22, FastEthernet0/0
Now say u apply an offset-list to increase the metric for the route 2.2.2.0/24 by 3 hop counts
On R1
access-list 1 permit 2.2.2.0 0.0.0.255
router rip
version 2
offset-list 1 in 3 FastEthernet0/0
R0#sh ip route
2.0.0.0/24 is subnetted, 1 subnets
R 2.2.2.0 [120/4] via 10.10.10.2, 00:00:12, FastEthernet0/0
from the output you can see that the metric has increased. This way it can be used to prefer a certain path
HTH
Narayan
