A random access file is a file in which you can "jump" anywhere inside it, without having to read sequentially to the position in which you are interested.
For example, let's say that you have a 1MB file, and you are interested in 5 bytes that start after 100k of data. The random access file will allow you to "go" to the 100th position in one operation. A non-random access file will require first reading 100 thousand bytes, and then reading the data you are interested in.
Hope this helps.
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