To Realize
To Notice
godan verb
When you attach your energy (imagine someone suddenly looking up at something, attaching their energy to it), you have noticed or realized something. That's why this word means to realize or to notice.
Don't confuse this with 気を付けて which is similar in that it has all the same kanji. It's just used a little different. Try to remember the difference before moving on.
The readings come from the 気 kanji (which you know) and the word 付く which you should know by now. Combine these together and you have the ability to read this word. Take note that the 付く part is rendaku'd, though, so it is a tiny bit different.
私に気付く
to notice me
気持ちに気付く
to become aware of feelings
そのことに気付く
to notice that matter
その女が自分の母だと気付くまでに時間がかかりました。
It took me some time to realize that the woman was my own mother.
気づいたらもう学校に行く時間だった。
When I noticed, it was already time to go to school.
あんたが私にアイスクリームをくれるなんて、本当に信じられないよ。あんたがそんなに優しいなんて今まで気付かなかったわ！
I can’t believe you gave me your ice cream. I didn’t realize that you were so kind until now.