Data packets often have to go through routers (more generally: 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).
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The distance between two hosts. The hop count n means that n gateways separate the source host from the destination host.
In IPv4 known as "time to live", and "Hop Limit" in IPv6, this field 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.
Routing term used for the next gateway to which packets should be forwarded along the path to their final destination. One technique to make content of a routing table smaller is called next-hop routing.
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.