TTL is the standard way of putting a limit on the number of hops a packet can be passed. Setting a TTL to 7 sets your Horizon to 7 hops.

This means that you can't "see beyond" 7 host hops. If we did not have a TTL or similar mechanism every packet would be passed on forever.

This would result in an everincreasing number of packets on the internet. If no packets were ever discarded the number of packets would very quickly shutdown every router on the internet.

Hope this helps