Targetting Ads to Existing Customers and Past Visitors
It’s possible to target search adverts in Google to individual customers. Certain keywords you are bidding on may perform poorly to new customers, largely because there is lots of irrelevant traffic. However if you could target an individual you already know is interested in you, this issue can be negated.
Google provides this facility via Remarketing Lists For Search Ads (RLSA). The link will take you to their guide.
This tool is based on the same capability used in Display Adverts (adverts which appear on certain websites) which has now been made available on the Search network (where adverts appear in search results pages).
The great benefit of this is to target existing customers, for example with further offers, or you can target specifically those users that visited but did not purchase, for example who may have abandoned their check-out. You have the choice.
To make such a user-targeted advert appear you first need to create a remarketing list and add a bit of code called a remarketing tag to your site. These adverts are controlled separately to your existing keywords you are bidding on.