en_tn_lite_do_not_use/heb/11/13.md

without receiving the promises

This speaks of promises as if they are objects that a person receives. Alternate translation: "without receiving what God had promised them" (See: rc://en/ta/man/translate/figs-metaphor)

after seeing and greeting them from far off

Future promised events are spoken of as if they were travelers arriving from far away. Alternate translation: "after learning what God will do in the future" (See: rc://en/ta/man/translate/figs-metaphor)

they admitted

"they acknowledged" or "they accepted"

they were foreigners and exiles on earth

Here "foreigners" and "exiles" mean basically the same thing. This emphasizes that this earth was not their true home. They were waiting for their true home that God would make for them. (See: rc://en/ta/man/translate/figs-doublet)