It is an editorial mark, provided by the editorial committee for the edition. The paragraph marks for the newer KJV study bibles tend to be the same, but some differ from the paragraph breaks of the Authorized KJV of 1611.
The 1599 Geneva Bible was the first to number the verses, and each verse was its own paragraph.
"The Geneva Bible was the first English Bible to use both modern chapter and verse divisions for the whole Bible. The New Testament verses in the Geneva Bible followed the verse divisions of Estienne’s 1551 Greek New Testament. Each verse was a new paragraph." Source: here.
The ¶ mark is inserted in the 1599 GNV in larger text sections to denote a break in activity or thought. It is a product of the editorial committee.
This became a standard for use in subsequent translations, but each editorial committee made its own determination. The paragraph breaks in the KJV sometimes agree with those of the 1599 GNV, but frequently deviate.
Punctuation was introduced in written documents around the 3rd century BC to provide the suggestion to the orator for breathing pauses, and eventually began to include other marks for tonal quality such as exclamation points and question marks. The marks were an addition to the written text by the orator, to aid in public speaking.
"The importance attached to the individual reader’s interpretation of a text was so great, in fact, that not a single surviving manuscript prior to the Middle Ages has been found to be punctuated in the writer’s own hand;10 only when a reader prepared a text to be delivered aloud would it be annotated as such." Souce: Pilcrow Part 1
Overall, the insertion of the pilcrow appears to be independently determined by each committee of the translation.
The pilcrow (¶) has an interesting history, and was gradually derived from the capitulum used by monks to mark new chapters and later used for new paragraphs or sentence markers, as the writer / scribe determined appropriate.
"At first used only to mark chapters, it star¬ted to pep¬per texts as a para¬graph or even sentence marker so that it broke up a block of running text into meaningful sections as the writer saw fit. ¶ This style of usage yielded very compact text,19 harking back, perhaps, to the still-recent practice of scriptio continua. Ultimately, though, the concept of the paragraph overrode the need for efficiency and became so important as to warrant a new line† — prefixed with a pilcrow, of course, to introduce it." Souce: Pilcrow Part 2
An interesting note is that the last pilcrow of the English translations occurs at Acts 20:36. Some have speculated that the original typesetters ran out of pilcrows and could not use them in the rest of the Bible. Others have determined some divine intervention in the discontinued use throughout the epistles and Revelation. See "The Last Paragraph Mark" here.
It is more likely that the epistles were short enough that the verses were sufficient to serve as space markers and paragraph breaks. But, I have not found any paragraph marking in Revelation in any of my KJV's.
Additional source info on the disuse of the pilcrow in printed type: Pilcrow Part 3