Transferring a domain can mean two things: switching the domain name to another registrar, or altering the domain record to make the domain point to a new host. We are concerned with the second definition. A domain has to be told which web host to direct visitors to, and this is done by changing the domain's name server records.
For example, say you purchased a hosting account at wonderfulhosting.com. They tell you to put their name servers in your domain record. These name servers might look like:
ns1.pdhwebdevelopment.com (192.185.12.147)
ns2.pdhwebdevelopment.com (192.185.12.151)
You will then visit your domain registrar's home page, sign in, and edit your domain record. Each registrar is different, but there will be fields in your domain record called "name severs," "primary/secondary name servers," etc. The registrar may or may not ask for the IP address of the name servers (192.185.12.147 and 192.185.12.151). It takes 12-48 hours for the change to take effect.
