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
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