What is the Hop (TTL-Time To Live) ?

Data packets often have to go through routers (gateways), if not several, before they reach their final destination. Each time packets are passed to the next router a hop occurs. (To see how many hops it takes to get from one host to another ping or traceroute/tracepath commands can be used).

The distance between two hosts. The hop count n means that n gateways separate the source host from the destination host.
Hop Limit

In IPv4 known as time to live, specifies a limit on the number of hops a packet is allowed before it should be discarded. this prevents packets from following a loop forever.
Next Hop

Routing term used for the next gateway to which packets should be forwarded along the path to its final destination.
Next Hop Forwarding

A routing table usually contains the IP address of a destination network and the IP address of the next gateway (next hop) along the path to the final network destination. Using a routing table to store a next hop for each 'Known' destination is called next-hop forwarding. Therefore a given gateway only knows one step along the path, not the complete path to a destination. It is also key to know that the next hops listed in a routing table are on networks to which the gateway is directly connected to.