RLSA or Remarketing List for Search Ads is a great concept to maximize the value of your existing visitors, who didn't take desired action(s). When they search again on Google, an advertiser can cutomize the ad copy or bid to draw attention. In fact, one can also target more broader keywords subsequent searches through RLSA knowing that the person had earlier shown interest.
However, the strategy or approach to implement RLSA is not so simple and must be thought through to realize true potential of RLSA campaigns. Here's a detailed article on RLSA, which will answer most of your queries:
Hope this helps. Feel free to ask any further query related to RLSA.