What is the use of "multiValued" field type in Solr?

A multivalued field is useful when there are more than one value present for the field. An easy example would be tags, there can be multiple tags that need to be indexed. so if we have tags field as multivalued then solr response will return a list instead of a string value. One point to note is that you need to submit multiple lines for each value of the tags like:

<field name="tags">tag1</tags>
<field name="tags">tag2</tags>
...
<field name="tags">tagn</tags>

Once you have all the values index you can search or filter results by any value, e,g. you can find all documents with tag1 using query like

q=tags:tag1

or use the tags to filter out results like

q=query&fq=tags:tag1

multiValued defined in the schema whether the field is allowed to have more than one value.

For instance:
if I have a fieldType called ID which is multiValued=false indexing a document such as this:

doc {
  id : [ 1, 2]
  ...
}

would cause an exception to be thrown in the indexing thread and the document will not be indexed (schema validation will fail).

On the other hand if I do have multiple values for a field I would want to set multiValued=true in order to guarantee that indexing is done correctly, for example:

doc {
  id : 1
  keywords: [ hello, world ]
  ...
}

In this case you would define "keywords" as a multiValued field.