To exchange things such as greetings, messages, or words; to exchange communication or feelings.
駅で旧友と挨拶を交わした。
I exchanged greetings with an old friend at the station.
二人は短い手紙を交わして別れた。
The two exchanged brief letters before parting.
会議のあとで名刺を交わす時間があった。
After the meeting there was time to exchange business cards.
To intersect, cross, or interlace (e.g., swords, lines, gazes); can describe physical crossing or meeting.
試合で二人の剣が激しく交わした。
In the match, the two swords clashed fiercely.
向かい合って目を交わすと、無言で頷いた。
Facing each other, they exchanged glances and nodded without a word.
As a suffix attached to the masu-stem of a verb, it indicates doing something with one another — roughly equivalent to “to each other” or “mutually ~”.
通りですれ違った人と軽く会釈をし、少し話し交わした。
I nodded slightly to the person I passed on the street and exchanged a few words.
手を振り合い、最後にもう一度握手を交わした。
They waved to each other and finally exchanged one last handshake.