What actually happens after you import
Gmail typically connects to the other account over POP (and sometimes IMAP), checking it periodically and copying new messages into your Gmail inbox. You can also label imported mail automatically and optionally send replies that appear to come from that other address, all without leaving Gmail.
Import versus forwarding
Importing is different from setting up mail forwarding: forwarding pushes new mail from the old account into Gmail automatically going forward, while the import wizard here can also pull in existing older messages already sitting in the other inbox. Many people set up both together for a complete migration.
Frequently Asked Questions
Does importing disable the original email account?
No. The original account keeps working normally; Gmail simply makes a copy of its messages available inside your Gmail inbox.
Is this the same as switching between multiple Gmail accounts?
No. Account switching keeps inboxes separate and lets you jump between them; importing merges another account's mail directly into a single Gmail inbox.