Shiny can run as a standalone application on your local computer, on a server that can provide shiny apps to multiple users (using shiny server), or on shinyapps.io.
install.packages("shiny")
if installing from CRAN, or devtools::install_github("rstudio/shiny")
if installing from the RStudio Github repository. The Github repository hosts a development version of Shiny which can possibly have more features when compared to the CRAN version, but it may also be unstable.