Many shuls let people claim (buy) seats and put their name on the chair where they usually sit, making it "officially" their makom kavuah. Some of Mi Yodeya's other makom-kavuah questions also indicate that someone can claim a specific seat.
However, my father once told me that makom kavuah doesn't mean claiming a single specific seat - it's an area, a certain part of the shul where you usually sit.
What is the halachic definition of a makom kavuah? (Plus sources.)
There are two unrelated issues being conflated here. One is the halacha of makom kavuah. Your father is correct that it does not need to be a specific seat, as the Mogen Avrohom 90:34 writes that makom kavuah is satisfied within 4 amos.
However, if you buy a specific seat, then you have a right to that seat. I am not buying a "makom kavuah" but rather a specific place (or the rights to use a specific place at a certain time) in the Shul.
For one example in halachic literature where the exact location of the seats is clearly discussed, see Minchos Yitzchok 9:154 where he discusses the exact number of seats away from the wall or the aisle. The person bought and has a right to exactly the 10th seat or whichever seat it is.
While we're on the topic, I once saw a fascinating teshuva in which someone had purchased the aisle seat, and then the wall was knocked down and more seats were added. He claimed that he had the right to the aisle seat and the shul said that his seat was in its original location and the new aisle seat was theirs to sell. The Rov who was asked brought a very interesting proof - when the yud was taken from Sarai's name and replaced with the hey, the yud complained, and was consoled by being added to the beginning of Yehoshua's name. However, isn't this a violation of the rights of the hey which was at the front of Yehoshua's name, and is now second? You see from here that being at the front is not a right that has standing. (If I find where the Teshuva was, I'll source it)
Vayifga Bamakom quoting Magain Avraham 42 says that anything within an 8 Ama radius is considered the Makom Kavua.
