Good question. Because I am a native Japanese but I have never thought about it. Although there would be some exceptions; in general, this is a Japanese expression to describe someone else. If I translate it directly into English, it is gonna be like this. 私、たけしさんの事が好き = I like about Takeshi-san. 私は、あなたの事が好き = I like (all) about you. Other examples for "～の事が（を、は） あなたの事を教えて = tell me about yourself. 私の事は知らないでいい = you don't need to know about me. You can say "あなたが好き"　or "あなたの事が好き." They both means basically the same, even though like I explained that they mean "like" and "like about." We, the Japanese, use them as more or less as the same expression. However, if you use ～の事が, the expression sounds more like talking about specifically humanbeings. Because we dont say,　私は犬の事が好きです(I like about dogs) or 　私はスイカの事が好きです(I like about water melon). "～が好きです" is more expression for general things and human, and "～の事が好きです" is tend to be used more specifically for humanbeings.

の is particle meaning possession. こと is thing. It literally means "I like things of Takeshi," but the meaning is little bit different. たけしさんが好きです also works. But you can't tell whether "I like Takeshi" or "Takeshi likes someone" from the sentence. Also, たけしさんが好きです sounds a little bit direct for me. のことが makes the expression softer than without. I wanna be said としくんのことが好きだよ from hot girls haha~