Well, there are a couple of ways to identify your incoming traffic. Although all of these methods are guesstimates, they do however provide an approximation to the source of your traffic.
- Tools such as SEMrush, Sistrix and other keyword position tracking tools
- Google Webmaster Tools Console
- Google AdWords Keyword Planning Tool
The last one being a hit or miss method, since it only shows how much search volume exist for keywords where specific pages of yours could have a high enough Quality Factor to be able to bid on.
Look at your Google Webmaster Tools Console, and look for your traffic spike in form of clicks and impressions. This should give you an idea which URLs of yours got promoted. This on the other hand might give you a sense of which keywords are associated with these URLs. If for some reason you can't identify a real spike, but rather a broad long-tailish increase in traffic affecting many URLs, then keyword position tools might help you out (i.e. Sistrix). These monitor the SERPs for keywords for which your pages are found and track any changes in position, also giving you a good indication for which keywords your URLs are found, what position they currently are found at and which URLs are displayed to searchers.
Then you could correlate your newfound information with Google Analytics and you got your pages and their correlating keywords.
Wow, I just realised this question was 5 years old. Nothing to see here, move along.