Your pattern doesn't match your example URL. Assuming your example URL was correct, you wanted this instead:
Options +FollowSymLinks
RewriteEngine on
# We want to rewrite requests to "/page/name" (with an optional trailing slash)
# to "index.php?p=name"
#
# The input to the RewriteRule does not have a leading slash, so the beginning
# of the input must start with "page/". We check that with "^page/", which
# anchors the test for "page/" at the beginning of the string.
#
# After "page/", we need to capture "name", which will be stored in the
# backreference $1. "name" could be anything, but we know it won't have a
# forward slash in it, so check for any character other than a forward slash
# with the negated character class "[^/]", and make sure that there is at least
# one such character with "+". Capture that as a backreference with the
# parenthesis.
#
# Finally, there may or may not be a trailing slash at the end of the input, so
# check if there are zero or one slashes with "/?", and make sure that's the end
# of the pattern with the anchor "$"
#
# Rewrite the input to index.php?p=$1, where $1 gets replaced with the
# backreference from the input test pattern
RewriteRule ^page/([^/]+)/?$ index.php?p=$1