Acronym for Multi Exit Discriminator and otherwise known as "Metric" in the BGP table.
The lower the MED the more preferred.
It is an optional non-transitive attribute.
Can dictate how other AS enter your AS.

Configure R4 so that it will advertise a MED value of 30 to R3 and 20 to R2. Afterwards,
tweak the route map to set a MED of 10 for network 144.144.144.144/32 in R4 towards R3. The end
result should have traffic from AS123 to 4.4.4.4/32 and 44.44.44.44/32 take R2 but traffic for
144.144.144.144/32 should take R3. At the start BGP has been established on all routers.
To start lets configure 2 route maps and set the MED as required.
R4(config)#access-list 20 permit any
R4(config)#access-list 30 permit any
R4(config)#route-map R2SETMED20 permit 10
R4(config-route-map)#match ip address 20
R4(config-route-map)#set metric 20
R4(config-route-map)#route-map R3SETMED30 permit 10
R4(config-route-map)#match ip address 30
R4(config-route-map)#set metric 30
Access-list matches all routes. Now, lets apply the route map to the neighbors.
R4(config-router)#neighbor 24.24.24.2 route-map R2SETMED20 out
R4(config-router)#neighbor 34.34.34.3 route-map R3SETMED30 out
Its in the "out" direction because R4 is the one advertising the routes. Let's check what R2 and R3 see in their BGP table.
R2#sh ip bgp
BGP table version is 31, local router ID is 24.24.24.2
Status codes: s suppressed, d damped, h history, * valid, > best, i - internal,
r RIB-failure, S Stale
Origin codes: i - IGP, e - EGP, ? - incomplete
Network Next Hop Metric LocPrf Weight Path
*> 4.4.4.4/32 24.24.24.4 20 0 4 i
*> 44.44.44.44/32 24.24.24.4 20 0 4 i
*> 144.144.144.144/32
24.24.24.4 20 0 4 i
R3#sh ip bgp
BGP table version is 10, local router ID is 34.34.34.3
Status codes: s suppressed, d damped, h history, * valid, > best, i - internal,
r RIB-failure, S Stale
Origin codes: i - IGP, e - EGP, ? - incomplete
Network Next Hop Metric LocPrf Weight Path
*> 4.4.4.4/32 34.34.34.4 30 0 4 i
*> 44.44.44.44/32 34.34.34.4 30 0 4 i
*> 144.144.144.144/32
34.34.34.4 30 0 4 i
Ok, its clear that the Metric now is changed to 20 and 30 for R2 and R3 respectively. Let's see how R1 sees the routes.
R1#sh ip bgp
BGP table version is 34, local router ID is 13.13.13.1
Status codes: s suppressed, d damped, h history, * valid, > best, i - internal,
r RIB-failure, S Stale
Origin codes: i - IGP, e - EGP, ? - incomplete
Network Next Hop Metric LocPrf Weight Path
*>i4.4.4.4/32 24.24.24.4 20 100 0 4 i
* i 34.34.34.4 30 100 0 4 i
*>i44.44.44.44/32 24.24.24.4 20 100 0 4 i
* i 34.34.34.4 30 100 0 4 i
*>i144.144.144.144/32
24.24.24.4 20 100 0 4 i
* i 34.34.34.4 30 100 0 4 i
R1 sees two paths, but notice that the paths with ">" are with those with lower MED. Therefore it is going to take those paths. Now, lets configure R4 so that the path R1 will take to 144.144.144.144/32 in R4 will be through R3 then clear the BGP session after.
R4(config)#access-list 33 permit 144.144.144.144 0.0.0.0
R4(config)#route-map R3SETMED30 permit 10
R4(config-route-map)#match ip address 33
R4(config-route-map)#set metric 10
R4(config-route-map)#route-map R3SETMED30 permit 20
R4(config-route-map)#match ip address 30
R4(config-route-map)#set metric 30
R4#clear ip bgp *
Now, lets see the outputs.
R2#sh ip bgp | beg Network
Network Next Hop Metric LocPrf Weight Path
*> 4.4.4.4/32 24.24.24.4 20 0 4 i
*> 44.44.44.44/32 24.24.24.4 20 0 4 i
*> 144.144.144.144/32
24.24.24.4 20 0 4 i
R3#sh ip bgp | beg Network
Network Next Hop Metric LocPrf Weight Path
*> 4.4.4.4/32 34.34.34.4 30 0 4 i
*> 44.44.44.44/32 34.34.34.4 30 0 4 i
*> 144.144.144.144/32
34.34.34.4 10 0 4 i
R1#sh ip bgp | beg Network
Network Next Hop Metric LocPrf Weight Path
* i4.4.4.4/32 34.34.34.4 30 100 0 4 i
*>i 24.24.24.4 20 100 0 4 i
* i44.44.44.44/32 34.34.34.4 30 100 0 4 i
*>i 24.24.24.4 20 100 0 4 i
*>i144.144.144.144/32
34.34.34.4 10 100 0 4 i
* i 24.24.24.4 20 100 0 4 i
We can see a change in R3 that shows a MED of 10 for 144.144.144.144/32, while R1 shows the same and will now take R3 to reach the subnet.