Yes you can, files can be securely shared with internal and external contacts just as you would with DropBox or Google Drive.
In your OneDrive select the file you wish to share and then click on the Share button. This will take you to the invite window. Simply add either the recipients name, username or email address. Choose if you wish to allow them to view or edit the file and once happy click the blue Share button.
You can also view/download a .PDF guide from Microsoft that shows these steps in more detail for sharing files with internal and external people.