The 14-day click window means that a user will be attributed to an ad if the user installs your app and has a session within 14 days of clicking on an ad. If the user has their first session 15 days or later after clicking the ad, the user will not be attributed to that ad.
If you advertise on Twitter, you should be aware that Localytics also employs a one-day view-through window for Twitter advertising. This means that if a new user views an ad on Twitter (but does not click the ad) within one day of their first session, Localytics will attribute the new user to Twitter.
Localytics operates on a 'last engagement' attribution model. This means that if a new user clicked on two ads before they started using your app, Localytics will attribute the new user to the more recently-clicked ad.