A phone that has two SIM card slots.
As a SIM links a phone to a specific carrier (service provider), billing account, and phone number, a dual-SIM phone can be linked to two different phone numbers associated with two different billing accounts. Those accounts and phone numbers can be with different carriers, and even in different countries.
One common use is to use one phone with both a business phone number (and account and a separate personal line. Another use is to have accounts with carriers in two different countries, in order to take advantage of favorable rates for local versus international calls, or to permit favorable rates for people calling you, by have local phone numbers in two countries.
Some dual-SIM phones only allow one SIM to be active at a time, requiring the user to switch SIMs via a menu option. Other phones allow both SIMs to be active at once, a feature sometimes called "dual-active".
Dual-SIM phones are uncommon in the U.S., but popular in certain other countries.