Olynyk has a cap hold of $7,735,035, which is 250% of his salary this season.
A cap hold exists as a placeholder salary for your own free agents. The amount is typically based on a percentage of a players most recent salary, and is always higher than it, as it's assumed that the player would get a raise. Teams are allowed to go over the salary cap to re-sign their own free agents, but they want to prevent teams from completely taking advantage of this rule, which would happen if the players were treated as having zero salary.
It remains on the books until one of two things occur: the team informs the league that they will not be exercising their right to go over the cap to re-sign the player (known as "renouncing"), or the player signs with a different team.
So with the case of Olynyk, on July 1st he will have a cap hold as described above. The Celtics will also likely extend a qualifying offer, which is a one-year contract offer at a salary prescribed by the CBA (in Olynyk's case that amount is $4.279,021). If the qualifying offer were greater than the 250% cap hold (which can sometimes happen for late 1st round or 2nd round players who pan out), the qualifying offer would replace the cap hold.
So while the Celtics and Olynyk are sorting through their options, Olynyk's hold would remain on the books. If the Celtics agree to a deal with a max free agent, they would rescind Olynyk's qualifying offer and renounce his free agent rights, making him an unrestricted free agent. Note that they cannot rescind his qualifying offer after July 15th -- another new change in the CBA.
Olynyk could of course throw a wrench into the Celtics plans and accept his qualifying offer before they rescinded it, but $4.3 million for Olynyk is a bargain, and he's certain to find something better in free agency.