Carry-on luggage is generally broken into two categories - "Cabin bags", and "Personal items".
There's no strict definition of these terms even within a single airline, let alone across the industry, but in general a "cabin bag" is a larger item that would go in the overhead bins, whilst a "presonal"personal item" is a smaller item that would go under the seat in front of you.
Most airlines generally allow (economy) passengers to bring one of each item - one bag plus one personal item, with the expectation that the larger bag would go into the overhead locker, and the smaller item under the seat.
By restricting carry-on to a single personpersonal item Turkish Airlines is likely looking to achieve a few different things.
Speeding up and simplifying the boarding process. Presuming most people put their personpersonal item under the seat in front of them, then this will be much faster than having to find space in the overhead lockers and put one item there, then subsequently still have to carry a second item to their seat. The simple fact people are carrying less as they board the plane will also make things a little faster and likely reduce much of the friction that occurs during boarding as passengers try and get past others who are busy stowing their bags.
Reduce people leaving their seats during the flight to get something from their bags in the overhead. With fewer bags in the overheads, there will be less need for people to stand up and access them (which often also requires others to get out of their seats).
Speeding up and simplifying disembarkation. Similar to boarding, less time will be wasted with people finding and reclaiming their bags from the overheads.
All of these will help reduce the number of people that are coming in close contact with others to at least some extent. Whether it's truly enough to make a difference is something that most likely can't be shown one way or another.