Refers to anything whose length can vary. For example, in databases, a variable-length field is a field that does not have a fixed length. Instead, the field length varies depending on what data is stored in it.
Variable-length fields are useful because they save space. Suppose, for example, that you want to define a NAME field. The length of each NAME field will vary according to the data placed in it. For example, John Smith is 10 characters long, but Thomas Horatio Jefferson is 24 characters long. With fixed-length fields, you would need to define each field to be long enough to hold the longest name. This would be a waste of space for records that had short names. With variable-length fields, the NAME field in each record would be just long enough to hold its data.
The opposite of variable length is fixed length.