What is the semicolon reserved for in URLs?

There is an explanation at the end of section 3.3.

Aside from dot-segments in hierarchical paths, a path segment is considered opaque by the generic syntax. URI producing applications often use the reserved characters allowed in a segment to delimit scheme-specific or dereference-handler-specific subcomponents. For example, the semicolon (";") and equals ("=") reserved characters are often used to delimit parameters and parameter values applicable to that segment. The comma (",") reserved character is often used forsimilar purposes. For example, one URI producer might use a segment uch as "name;v=1.1" to indicate a reference to version 1.1 of "name", whereas another might use a segment such as "name,1.1" to indicate the same. Parameter types may be defined by scheme-specific semantics, but in most cases the syntax of a parameter is specific to the implementation of the URI's dereferencing algorithm.

In other words, it is reserved so that people who want a delimited list of something in the URL can safely use ; as a delimiter even if the parts contain ;, as long as the contents are percent-encoded. In other words, you can do this:

foo;bar;baz%3bqux

and interpret it as three parts: foo, bar, baz;qux. If semicolon were not a reserved character, the ; and %3bwould be equivalent, so the URI would be incorrectly interpreted as four parts: foo, bar, baz, qux.

The intent is clearer if you go back to older versions of the specification:

  path_segments = segment *( "/" segment )
  segment       = *pchar *( ";" param ) 

Each path segment may include a sequence of parameters, indicated by the semicolon ";" character.

I believe it has its origins in FTP URIs.

Section 3.3 covers this - it's an opaque delimiter a URI-producing application can use if convenient:

Aside from dot-segments in hierarchical paths, a path segment is considered opaque by the generic syntax. URI producing applications often use the reserved characters allowed in a segment to delimit scheme-specific or dereference-handler-specific subcomponents. For example, the semicolon (";") and equals ("=") reserved characters are often used to delimit parameters and parameter values applicable to that segment. The comma (",") reserved character is often used for similar purposes. For example, one URI producer might use a segment such as "name;v=1.1" to indicate a reference to version 1.1 of "name", whereas another might use a segment such as "name,1.1" to indicate the same. Parameter types may be defined by scheme-specific semantics, but in most cases the syntax of a parameter is specific to the implementation of the URI's dereferencing algorithm.