Bech32 is an address format that was defined in BIP-173 in March of 2017 and included along with SegWit in Bitcoin’s code. BTG forked from Bitcoin after SegWit activated, so Bech32 addresses have been supported in BTG since launch.
Any wallet or service which allows a “SegWit” address is using Bech32.
(Bitcoin Cash forked from Bitcoin after SegWit and Bech32 were already in the code base, but before SegWit activated. Bitcoin Cash chose to strip out SegWit and Bech32 at the time of their fork, but several months later added their own new address scheme, cashaddr, which is based on Bech32.)
Why the new format?
The prior Bitcoin address scheme used a base58 numbering scheme (often called “normal” or “legacy” addresses), while Bech32 uses base32, and base32 makes it more compatible with other systems. For example, it more easily maps to normal alphanumerics, it consumes less space in QR codes, and it’s more easily human-readable (the specification also provides for a human-readable identifying tag in front of the address.) Bech32 addresses also include internal error-correction ability.
In short, it’s a better address scheme for a variety of reasons.
The Name
Bech32 is named for the Bose–Chaudhuri–Hocquenghem code scheme (often called BCH codes, pronounced “bech codes”) and the base32 numbering system. BCH codes were discovered and described in 1959 and 1960, not to be confused with the exchange symbol “BCH.”.