It's called a "long s" and this is the character you say is similar to an f " ſ ". It was used when there was an "s" at the beginning or in the middle of a word as in Greek initial and medial σ and the final ς.

For instance the German Eszett ß is a development of the ligature of "ſs", that's why it's also known as double s and the last name Gauss is written as Gauß in german along many other words.

I don't know much about its decline but i hope this helps :)

"Round s" (modern) and "tall/long s" (looks like an f) actually both evolve out of Roman script--so it's common in manuscripts starting around 30 BC and into the very very early Middle Ages, although they're probably older as letter forms. Round s was used for capitals, which in Latin paleography means formal writing; tall s was used in cursive, so less formal, faster writing. You can definitely see how the tall s takes less time to write!

As different styles of handwriting (fonts, basically) waxed and waned in popularity throughout the Middle Ages, so too did the long and tall s. Some "hands", the technical term, even mixed the two. The second word here is "p[rae]sentes"--you can see how the second letter is a tall s and the final letter is a round s. (excerpt from 1388)

With the invention of the printing press, printers typically sought to recreate the manuscript traditions their audiences were familiar with. Although obviously book production evolved quickly, certain remnants of manuscript culture and handwriting remained--including the two s forms. You can see the same system from the 1388 manuscript with "Pass and Repass" in this printed 1766 document--the tall s occurs in the middle of the word, the round s on the end.

Sources: A neat book on paleography with great examples (entire reproduced manuscript pages) is Michelle Brown, A Guide to Western Historical Scripts from Antiquity to 1600. I borrowed the images from the University of Nottingham's Manuscripts and Special Collections department.

https://i.imgur.com/ajw4h54.jpg