Traditionally, level editing is done using some kind of standalone tool that is not part of the game engine. The level designer loads the level, makes changes to it, and exports it to see how it plays in the game.
This level-editing tool might be a commercial product, such as 3ds Max, or it might be an engine-specific tool that comes with a third-party engine, or it might even be a custom in-house tool.
Level editors can be integrated with the game engine, allowing the designer to view and play the level as it's being edited. This is ideal from the point of view of rapid feedback, but the problems of edit conflicts and bottlenecks still remain. If two level designers want to edit the same part of the level, they usually will have to check out the entire level from the VCS.
With code, multiple checkouts of the same file are less problematic because it's relatively easy to merge text files automatically, as the changes are usually on well separated lines. Conflicts that cannot be resolved automatically are usually taken care of very easily manually, as the nature of the conflicting changes is readily apparent to the programmer who makes the merge.
Unfortunately, this solution does not work with level data, which is often stored in a binary format that's impossible to merge, especially if the level editing tool is some thing like 3ds Max.
Even if the level is stored in a text-based format, such as XML, it's much harder to merge as there are many internal dependencies and automatically generated data that create a broader mesh of changes that are difficult for a human to read. What we get are more conflicts, which then are much harder to resolve without breaking something.
The difficulty in merging changes in level or world files would inevitably lead to bottlenecks if no steps were taken to mitigate it. Various solutions have arisen to handle the problem. The simplest is to break the level down into the smallest chunks possible, so that individual level designers can check out only the sections of the level they need.
Using small chunks improves matters by reducing edit bottlenecks, but adds complication in how the level is split up and subsequently pieced together. Implementing high-level changes to large sections of a level also becomes difficult.
Though bottlenecks are reduced, they're not eliminated, as there will still be merge work needed at the borders of the areas assigned to individual level designers. Edits here must still be manually coordinated. The large number of individual parts that make up the divided level now places an undue organizational burden on the level designer.
Sometimes more ad-hoc solutions are used. A level might still be stored in one large file, but when two people need to work on it at the same time, it is manually split into two sections. The work is done (with some discussion to avoid conflicts), and then the two sections are visually merged back together.
Sometimes, special merge tools are written just for this purpose. This technique is fraught with problems, as the merging process is rarely simple, and can take some time.