DHCP or Dynamic Host Configuration Protocol is a service for automatically assigning an IP address and other parameters (Subnet Mask, Default Gateway, DNS Servers, WINS Servers, etc.) to a host. A host is any network aware device on the network (computer, printer, switch, etc.). Any host configured for DHCP will attempt to secure a lease from a DHCP server when the network interface comes on-line during the boot process.
The Lease Obtained line is the Date/Time stamp of the DHCP lease.
The Lease Expires line is the Date/Time when the lease is due to expire.
At one half the interval between the two, the client will start to attempt to renew its DHCP lease. If the renewal is successful, the time stamps will update. If the renewal is unsuccessful, the host will continue to use the same IP address and will attempt to renew the lease at a predifined interval until it succeeds.
When a renewal is successful, the host may be assigned a new IP address or it may continue using the previous IP address that was assigned. This action depends upon the configuration of the DHCP server. It used to be common for DHCP servers to force a new IP address at each renewal but these changes consume valuable processing resources -- a change requires about 8x the amount of CPU time and network bandwidth as a continue does -- so most DHCP servers no longer force a change of IP address at each renewal, often even if the host has been restarted (rebooted or disconnected from the network and reconnected).
An infrequently used paramater is Maximum DHCP Lease Time. It is specified in seconds though it's usually displayed in hours when it is set. If this parameter is not set, the host will attempt to renew an IP address indefinitely but will stay on the network with its current IP address. If the parameter is set, the host will stop renewal attempts when the Max DHCP Lease Time is exceeded at which time network communication will fail.