There are six parts of a bra, in my mind.
Let's break it down.
This is where you actually put your boob. A cup can be loose, wireless, shaped, wired, padded, push up, etc.
Maternity bras will also have the option of a drop down cup, to make breast feeding/milking easier.
Lots of fun stuff happening in there.
The wing is the bit that goes from the edge of your cup, under your arm. This is part of the band.
The band is the whole bit that connects from your cup to your hooks. This is a really good monitor of whether your bra is fitting correctly. If you have flesh spill over (AKA "back fat") that's super apparent, you might need a bigger band.
The hook is the part that actually keeps your bra together/on. Hooks can be in the front or back of the bra, and the number of hooks really varies with bra style, size, and maker. Only real exception to this part is a bandeau bra, which is just kind of an over the head number, that also lacks straps.
The strap is the part of the bra that generally keeps it from falling down to your waist, and these puppies are adjustable! Bras that have straps connected to the cup directly tend to lift from the actually shoulder, and less from the cup itself. Bra's that are strapless tend to have a line of rubber along the band and sometimes the cup.
The bridge is the connector between cups in the front. Sometimes the bridge is small, sometimes it's bigger. Some bra makers have convertible bridges to shift the breasts and give them more of a push up. The bridge can also be home to a front hook. Easy access!
So now we know the parts of the bra! Get ready for the pop quiz.