The moment a board has both "who" and "what state" crammed into the same columns, nobody can scan it in under ten seconds. Columns and swimlanes solve two different problems, and a board only stays readable when each dimension gets its own axis.
Columns are one dimension; most real work has two
A column answers "what state is this in" — To Do, In Progress, Done. That's enough until the board has more than one team, more than one workstream, or more than one type of work sharing the same statuses. At that point, a flat column view forces you to either split into separate boards (losing the shared view of overall flow) or cram a second dimension into card titles and colors (losing scannability). Swimlanes are the second axis: horizontal bands that group cards by owner, team, or work type, while columns still track status across all of them.
Swimlanes answer "whose work is stuck," columns answer "what's stuck"
These are different questions a team asks constantly, and a board with only columns can answer one of them well. With swimlanes, a quick glance answers both at once: which lane has the most cards piling up in one column tells you which team or workstream is the bottleneck, without anyone needing to ask out loud.
Don't lane by something that changes every day
The most common swimlane mistake is grouping by something unstable — by individual assignee on a team that reassigns work daily, for instance — which means the board's structure needs constant maintenance just to stay true. Lane by something relatively stable: team, project, work type, or priority tier. If a lane assignment needs to change more than once a sprint, it's the wrong dimension for a lane.
Two or three lanes beat eight
Swimlanes solve the "too much in one view" problem, but adding too many recreates it — eight thin lanes are no more scannable than one crowded column. If you need more than three or four lanes to represent your structure, that's usually a sign the board itself should split, with a higher-level view rolling up status across the separate boards instead.