A feature of some newer (2015 and on) networks and phones that enables interoperability between phones and networks that are designed for overlapping frequency band definitions.
Before MFBI, a cellular base station (a "tower") operating at a given radio frequency could only "advertise" to phones that it supported one band definition, even if its frequency fell within two overlapping band definitions. This relatively small technical issue was a large barrier to phone/network compatibility.
For example, U.S. Cellular owns licenses for its LTE network to broadcast at 728-734 MHz. The only band definition that covers that range is "band 12", which covers 728-746 MHz. So the U.S. Cellular network and phones are designed for band 12. Meanwhile, AT&T operates part of its LTE network broadcasting at 734-746 MHz. Band 12 covers those frequencies, but so does band 17, which is defined as just 734-746 MHz, a subset of band 12. AT&T originally designed its network and phones to operate only as band 17. This meant that U.S. Cellular's band 12 phones could not connect to AT&T's band 17 network, even though both were otherwise perfectly capable of communicating at 734-746 MHz. MFBI allows AT&T's network to advertise to phones that it is both band 12 and 17. This relatively simple change allows band 12 phones to connect to AT&T's network.
Similar issues affect other frequency bands and other companies' networks, including T-Mobile and Sprint.
MFBI is a relatively new feature, introduced in 2015. Networks must be upgraded to support it. Phones must also specifically support MFBI to take advantage of it; older phones do not support it.