うまくいく
 

Hi, could someone explain to me what exactly does "うまくいく (Go well)" mean and use for?

Hi.

明日の母さんの手術がうまくいくか、とても心配だわ。 　
I'm worried about my mom's operation tomorrow.
きっとうまくいくよ。
I'm sure that it will go well. (Her operation will be successful, for sure.)

明日のスピーチが心配だよ。
I'm worried about the speech tomorrow.
きっとうまくいくって。
You'll surely go well. (You will make a good speech for sure.)

?????
Is this what you wanted?
I think うまくいく is identical to "go well".
What is in your mind to ask that?

edit) OK, I looked for my dictionary, which says;
come along●come along OK [okay]●come down big●come off well●come on●come out smelling like a rose●come over go down●come up roses〔【用法】通例 be coming up roses の形で用いられる〕●cut it〔通例、否定形で使われる〕●do well●do [turn] the trick●forge ahead●get along●get anywhere〔【参考】get someone anywhere〕●get cooking well〈俗〉●get on●get the lead out of one's ass [pants]〈卑〉●get the lead out of one's feet [it]〔【直訳】足から鉛(lead)を外す〕●go down a treat●go great●go over●go right●go smoothly●go together well●go well●hit it off (well)●kick ass [arse, butt]〈俗・卑〉●luck out●make out●pay off●perform well●ride on the crest of (the) wave●ring the bell●shape up〔【用法】通例進行形で〕●speak the same language●strike lucky●turn out good●turn out okay●turn out well●work a treat●work out●work out nicely●work out well
【自動】fly●prevail

This is one of those phrases that you can look at piece by piece and remember because the two parts individually translate exactly to the correct English phrase.

Honestly, if I didn't know this phrase already, and then you gave me a sentence that used うまくいく to mean "to go well," I would have suspected you were an early learner translating English to Japanese word-for-word.

うまい - good, well-done
いく - to go

うまくいく - to go well

Thanks for the help, guys. This is the kind of verb/phrase that I find it complicated and difficult to get the hang of it because it comes with far too many different meanings. Just like 交わる(Keep company with).