After you give your final go-ahead the developer will upload the website files to the server. This is called deployment. An FTP program will be used to do this. Some web development companies offer domain name registration and web hosting services as well. If you have no idea what any these mean, you could use their suggestion.
Once your accounts have been configured and the website files are successfully uploaded onto the server, the site will be put through one last run to make sure that all the files are uploaded correctly and the site is fully functional.
Depending on your website and the technology you want to use you can use shared hosting, VPS, cloud hosting or a dedicated server. Shared hosting is the cheapest option and a dedicated server is the costliest but if data security is your concern you should opt for this.