In just a few short sentences -
UEFI will replace BIOS in the near future. BIOS is old, started in the 1980's and of course the code was improved and evolved over a period of time.
However it still has serious limitations such as the size of the drive it is able to boot from, and the BIOS code has to run in the 16 bit mode - to name a few.
Hence the UEFI standard was brought in by Intel, AMD, M$ and a few others.
The UEFI overcomes the BIOS limitations - it can boot from much larger hard disks using GPT and can run in 32 or 64 bit mode.
Most UEFI implementations have a BIOS compatibility mode. Please read literature on UEFI if you need in-depth knowledge.