NVM is a tool to switch between multiple [[node]] versions. Each version is isolated, meaning packages are tied to the version of node used. Packages install to ~/.nvm/versions/node/<version>/lib/node_modules/, which nvm automatically adds to your PATH.
Without NVM you can only have a single installed version, and all packages are installed to somewhere in usr/, depending on the node version. Due to permissions, sudo may also need to be used.
NVM can be setup to automatically use the node version of the folder you're currently in (looking at files like nvmrc), or to a default which is set with nvm alias default.