If a packet enters a chain such as the INPUT chain in the filter table, we can specify a jump rule to a different chain within the same table. The new chain must be userspecified, it may not be a built-in chain such as the INPUT or FORWARD chain for example. If we consider a pointer pointing at the rule in the chain to execute, the pointer will go down from rule to rule, from top to bottom until the chain traversal is either ended by a target or the main chain (I.e., FORWARD, INPUT, et cetera) ends. Once this happens, the default policy of the built-in chain will be applied.
If one of the rules that matches points to another userspecified chain in the jump specification, the pointer will jump over to this chain and then start traversing that chain from the top to bottom. For example, see how the rule execution jumps from rule number 3 to chain 2 in the above image. The packet matched the matches contained in rule 3, and the jump/target specification was set to send the packet on for further examination in chain 2.
Userspecified chains can not have a default policy at the end of the chain. Only built in chains can have this. This can be circumvented by appending a single rule at the end of the chain that has no matches, and hence it will behave as a default policy. If no rule is matched in a userspecified chain, the default behaviour is to jump back to the originating chain. As seen in the image above, the rule execution jumps from chain 2 and back to chain 1 rule 4, below the rule that sent the rule execution into chain 2 to begin with.
Each and every rule in the user specified chain is traversed until either one of the rules matches -- then the target specifies if the traversing should end or continue -- or the end of the chain is reached. If the end of the user specified chain is reached, the packet is sent back to the invoking chain. The invoking chain can be either a user specified chain or a built-in chain.