Type-A is the classic USB plug as we have long known it. The chunky rectangular plug was the original design and it remains the standard plug for use at the host end of the USB cable.
Now Type-A has gone through a number of changes to accommodate different versions of USB, with more pins added to allow for the faster speeds of USB 3.0 for instance. However the fundamental design of the plug has remained the same, with the new connections incorporated in such a way that all USB Type-A plugs and sockets are compatible no matter which version of USB they use.
It’s not always the case that whatever you plug in will work, as the newer standards of USB also deliver more power, which may be required by whatever device you’re plugging in, but for the most part they’re completely interchangeable.
There are also some variations of Type-A including Mini Type-A and Micro Type-A but these were never widely adopted due to the complicating nature of having different types of USB socket on host devices. They are now deprecated.