In the example above, the speaker's apartment building isn't right next door to the playground. It's next to the building which is next to the playground. That means that her building is "one building over from" it.

You can use this expression to describe the location of anything that's arranged in a row. For example:

She lives two doors over from me.

There was shooting three blocks over from my house last week.

See the woman sitting two seats over from Jimmy? That's the director.

You can also include the direction:

See the woman sitting two seats to the left of Jimmy? That's the director.