IPA: /ˌɪn.tɪˈmeɪ.ʃən/
KK: /ɪnˈtɪmeɪʃən/
A hint or indirect suggestion about something, often not stated directly.
She gave an intimation that she might be leaving the company soon.
Intimation is formed from "in-" (meaning into or towards) and "tima" (from Latin "timere", meaning to fear or to be afraid). The word refers to a hint or suggestion that leads one to a realization or understanding, often subtly, as if guiding someone into a thought.
Think of being 'led into' ('in-') a realization or hint, which is what intimation means.