1To exchange greetings, words, letters, business cards, promises, etc. with someone; to trade communication or feelings back and forth.
初対面の二人は、まず名刺を交わした。
Meeting for the first time, the two of them first exchanged business cards.
隣の人とは毎朝、挨拶を交わす。
I exchange greetings with my neighbor every morning.
両社は署名して、正式に契約を交わした。
The two companies signed and formally entered into a contract.
見知らぬ人と二言三言、言葉を交わした。
I exchanged a few words with a stranger.
2To cross or interlace (blades, glances, etc.); to bring two things into intersection, as when swords clash.
二人の剣士は舞台の上で激しく刃を交わした。
The two swordsmen crossed blades fiercely on the stage.
両軍の武将が一騎打ちで太刀を交わした。
The generals of the two armies crossed swords in single combat.
3As a suffix on the masu-stem of a verb, it means to do the action with one another — e.g. 酌み交わす (to drink together), 見交わす (to exchange glances), 言い交わす (to exchange vows).
久しぶりに友と酒を酌み交わした。
I drank together with an old friend for the first time in ages.
二人はそっと目を見交わして微笑んだ。
The two of them quietly exchanged glances and smiled.