In Facebook Messengers listing of friends, you might see a time listed next to some of your friends name such as: 5m, 1h, or 2d (to the left of the mobile phone icon, either in the Favorites listing or when you do a Search). This time seems to correspond to when a person was last active on the Facebook Messenger app (and also currently includes the main Facebook iphone app, but does not include the Facebook website). Essentially, this time only seems to be an active time for when they were logged into the Facebook / Messenger mobile apps (or Facebook Messeger desktop app) and using it in some form or fashion (but not necessarily needing to send messages).
In other words, the time that is shown in the Facebook Messenger listings does not refer to when a person was just checking out facebook website, because you can notice friends who will go online using Chat with the green dot, but once they go offline you will not see a time listed next to their name in the Facebook Messenger list in the mobile app.
With that said however, if you click on a friends name in the Facebook Messenger list, it may actually display the last time that a person was logged into Facebook and interacted with the site in some manner, which could simply be clicking around on the site or app (this active time will include the iPhone app, online website, or on facebook Chat). It might give a minute or hour time or say "active now" just below the persons name. But once the person has logged out or closed out of facebook you will no longer see anything below this persons name, if they are not using the Facebook Messenger app.
So essentially, it seems as though, only Friends who are using the Facebook Messenger mobile app, will actually retain a time value (such as "active 1h ago" or "active 2d ago") in the Favorites or search listing or when you click on their name.
Lastly it appears that after about 4 days this time value is removed from the list if they have not logged into the Facebook mobile apps.