Si otra persona ha subido cambios en la misma rama que tú, Git no podrá subir tus cambios:
$ git push origin master
> To https://nombre de host/USERNAME/REPOSITORY.git
> ! [rejected] master -> master (non-fast-forward)
> error: failed to push some refs to 'https://nombre de host/USERNAME/REPOSITORY.git'
> To prevent you from losing history, non-fast-forward updates were rejected
> Merge the remote changes (e.g. 'git pull') before pushing again. See the
> 'Note about fast-forwards' section of 'git push --help' for details.
Puedes resolver este problema extrayendo y fusionando los cambios realizados en la rama remota con los cambios que has hecho localmente:
$ git fetch origin
# Fetches updates made to an online repository
$ git merge origin YOUR_BRANCH_NAME
# Merges updates made online with your local work
O bien, puedes simplemente usar git pull
para ejecutar al mismo tiempo ambos comandos:
$ git pull origin YOUR_BRANCH_NAME
# Grabs online updates and merges them with your local work