If you see a word that's confusing, look it up.
From dictionary.reference.com ............
suf·frage
   [suhf-rij] Show IPA
noun
1.
the right to vote, especially in a political election.
2.
a vote given in favor of a proposed measure, candidate, or the like.
3.
Ecclesiastical . a prayer, especially a short intercessory prayer or petition.
Origin:
1350–1400; Middle English < Latin suffrāgium voting tablet, vote, equivalent to Latin suffrāg ( ārī ) to vote for, support + -ium -ium
The connotation you quote obviously has nothing to do with voting, and is regarding church, or "ecclesiastical" matters (ecclesia is church, as in extra ecclesiam nulla salus).
One good trick is to replace the word with its definition, and then read the sentence again:
Both partial and plenary indulgences can always be applied to the dead, but only by way of a prayer, especially a short intercessory prayer or petition.
Hope that helps.