"Forward access context notification" and "Forward access context acknowledge" both messages sent over S10 interface from source MME to target MME and from target MME to source MME respectively. Forward access context notification message carry E-UTRAN transparent container information, which is nothing but PDCP SN receiver and transmitter status.
Please check the S1-handover call flow from 3GPP 23.401 spec.
source eNodeB sends "eNodeB status transfer" to source MME then MME sends this e-utran container to target MME in forward access context notification message. Once target mme receives this message, the received e-utran container information is sent to target eNodeB via mme status transfer message.
Hopefully above description will provide some more clarity to you.