The Masked Man is a recurring character whose main characteristic is the use of The Mask. His intentions are unknown, not being clear if he wants to help Jay and hurt Alex Kralie or if he is just trying to use one or both of them. Some believe he is totheark because he is seen in a few of his videos. He's called "Masky" by the fandom.
Far into the series, we learn that there are actually multiple masked people. The second most prominent masked person is the Hooded Man, and they seem to be working together.
Warning: Major plot twists and reveals are under spoiler tags.
The Masked Man first appears in Entry 18, when Jay goes to The House. He attacks Jay, and after a quick struggle falls to the ground while having a seizure. Jay carefully approaches him to remove his mask, but he shouts "No!", pushes him away and flees.
During Entry 23, Jay finds him again in The House, and the former begins to chase him through the house, causing what some people believe traveling through space and time when passing through a door.
During Entry 33, he slips into Jay and Jessica's hotel, enters Jay's room and seemingly attacks him. Jay hits him with a flashlight and flees with the recently found tapes. He's briefly seen limping, as it is confirmed in Entry 35. Some people says teleportation happens when Jay escapes. More info in Entry 33's Observations section.
After Jay's walk with Alex in the forest in Entry 50, the Masked Man is chased by Jay after being spotted lurking behind a tree. Jay is not able to catch him, despite his limping, which made some people reaffirm he has the ability to teleport. Jay loses him when he goes into The Tunnel.
As shown in Entry 35 the Masked Man is without a doubt, or one of them and he is executed in front of J… but the guys doing it looked like pros, could there be more of these situations? (Note: this theory has been proven false in Entry 36. Jay explicitly states the Alex broke Masked Man's leg then left him.)
In many entries it can be seen that video and audio distortion as well as amnesia occurs around the Masked man in a similar fashion to encounters to The Operator.
Possible reasons for this are:
The Masked Man has powers similar to The Operator
(how this occurs can have any number of theories)
The Operator is always present but hidden wherever Masky is
People who have had prolonged exposure to the effects of the The Operator's influence may begin to exhibit lesser effect to those around him/her
(Many theories state that the Masked man has had considerable contact with T.O. and may have become 'Electro-statically charged' in a sense.)