In most systems with proportional representation, each party has a numbered list of candidates. The list is determined by the party, usually through a party-internal process, and published before the election.
The seats gained by a party are then filled with the people from the party list in the stated order. For example, when Party A got 25 seats, they go to the 25 first people they put on their list. The people on these seats represent the party as a whole, not any particular district.
One property of this system which you might consider a disadvantage is that it puts a lot of power into the hands of the parties. The top list-candidates of a popular party are almost guaranteed to get into the parliament, no matter how unpopular they might be among party-sympathizers who are not party-members.
Another problem is that list-candidates don't represent any particular district.
That's why there are many variations of this system which give some power to nominate specific people back to the voters.
In German parliament elections, for example, people have two votes. One for the proportional representation and one for the local candidate. When a local candidate wins a district, that candidate must gain a seat owned by their party, no matter if they are on the party list or not. There are twice as many seats as voting districts. So only half the seats represent districts while the other half just represent the party as a whole. This system is well explained in the video Mixed-Member Proportional Representation by CGP Grey.
Other countries simplify this by unifying those two votes. Your vote for your local candidate is also a vote for the national party list. So when your local candidate loses, your vote still counts for the representation of the national party of that candidate.