The telesmurf was an invention Handy came up with to deal with the overgrown smurfmelon vines from Farmer's garden in "The First Telesmurf", when Papa Smurf's experimental smurfmelon seeds caused the vines to grow much longer than he intended them to.
Handy noticed that, because the vines were hollow, they were able to transmit sounds from one blossom to another across long distances. Taking that into account, Handy had the vines strung around poles throughout the village, with parts of the vine reaching into every Smurf's house so they could talk to each other without ever leaving their house, calling it the "telesmurf" -- a rather primitive Smurf version of the telephone called a speaking tube or a voice pipe, an invention credited to Handy, though it was Papa Smurf's smurfmelon seeds that made the vines and blossoms come about. To use it, a Smurf simply had to speak into a blossom, and then use the same blossom to hear the other Smurf's response.
Soon after the telesmurf went into operation, there were problems with it, such as noise pollution that came from too many Smurfs using it at once that was loud enough to keep Baby Smurf from sleeping and to give other Smurfs a headache. To counter this problem, the vines were rerouted to Brainy's house, where he served as the official operator who controlled who got to talk to whom at any time and how long they could talk for. But another problem of the telesmurf was that the smurfmelon vines had reached all the way to Gargamel's castle, where he could hear the Smurfs talking to each other through the telesmurf. Gargamel tried to use the sound of the Smurfs talking to find his way to the village, but only got halfway there when night fell, so he slept out in the forest right next to the vines, which transmitted his snoring. Thinking that the snoring noise was a bear, Papa Smurf sent Hefty and a few other Smurfs to prune back the smurfmelon vine, but soon Smurfette heard Gargamel talking in his sleep through the telesmurf, and told Papa Smurf about it. Handy had part of the smurfmelon vines tied so that they could no longer hear Gargamel, but now Hefty and some of his fellow Smurfs also found Gargamel out in the forest, who at this point was covered in smurfmelon vines. Gargamel struggled to break free of the vines before he and Azrael gave chase to the Smurfs, who then set up a trap to catch Gargamel in while they safely returned to the village.
The next day, though, the smurfmelon blossoms were now changing into fruit, thus marking the end of the telesmurf.
The "Telesmurf" also appeared in a one-page gag in Smurf Stories as an actual telephone; and the comic story "The Telesmurf", although in that adaptation, pumpkin seeds replaced smurfmelon seeds for the creation of the vines that were used in the invention.