Becoming acquainted with someone; an approach toward establishing closer relations. Often used with the honorific prefix 'お' (e.g., 'お近づきのしるしに').
お近づきのしるしに、手作りのお菓子を渡した。
As a token of getting acquainted, I gave homemade sweets.
彼との近づきは共通の友人のおかげだ。
My becoming close to him is thanks to a mutual friend.
新しい隣人と近づきになるのは時間がかかることもある。
It can take time to become acquainted with new neighbors.