Interpreting the reciprocal of $R_0$
1/R0 is the threshold fraction. If fraction of population vulnerable to particular infection is  more than 1/R0, only then infection can spread further. And if it is less than 1/R0 then infection can not progress and eventually goes away

And, 1-1/R0 is the fraction of population which requires vaccination so that we can have herd immunity.

(Reference
http://home.iitk.ac.in/~peeyush/mth426/Epidemiology.pdf 

https://www.slideshare.net/singh_br1762/r0-value-herd-immunity)