Every time you add a plugin to your website you’re adding more things to load, which has the potential to slow down your website.
But it’s not always as simple as more plugins = slower website.
Not all plugins are created equally as far as speed goes. You could have a website with 20 plugins that are all light and have it load faster than a website with 3 plugins that are bloated and resource-heavy.
Before adding any plugin to your website, search for it in WP Hive.
WP Hive is a user reviewed version of the WP depository, which scores all the plugins on speed, memory usage, and a load of other important metrics.