The confusion probably comes from the fact that each type of connector/cable is used for two different signal levels.
- XLR cables (three-conductor cables with XLR connectors on the ends) are used for both microphone level signals and line level signals.
- 1/4" TS cables (two-conductor cables with two-conductor 1/4" connectors on the ends) are used for instrument level and line level signals.
- 1/4" TRS cables (three-conductor cables with three-conductor 1/4" connectors on the ends) are pretty much only used for line level signals.
Many audio devices have 1/4" TRS jacks for line level input and output, many have XLR jacks for line level input and out, and many have both. Since it's not always predictable when there will be 1/4" TRS or XLR for line level signals, it's very helpful to keep some XLR (male and female) to 1/4" TRS adapter cables around.
Here's the thing, just because you can plug a cable in, using an adapter or not, does not mean the signal that you're sending on that cable is appropriate for the device you're sending it to.
You normally can't plug a microphone into a 1/4" TRS input, because microphones need mic preamps, and mic preamps pretty much universally have XLR inputs.
What you have is called a Neutrik Combo Connector, which is both an XLR input and a 1/4" TRS input on one connector. But those two inputs are connected to different electronics. The XLR input goes to a mic preamp and then to line-level processing before being amplified up to speaker level. The 1/4" TRS connector bypasses the mic preamp and goes right to the line level processing. Without the mic preamp, the mic signal is too quiet for the speaker. The reason why there is a 1/4" connector that bypasses the mic preamp is for line level signals.
Aside from connecting gear that has different connectors for the same kinds of signal, there's another big use case for XLR to TRS adapters. When you have a stage snake that is all XLR (my personal preference), and you want to connect devices with 1/4" TRS I/O on either end of that snake, then converting to XLR and back makes that easy.
One thing XLR cables can do that 1/4" cables can't is daisy chain, which means you can take two 25' XLR cables and plug them together to make a 50' XLR cable - without any adapters or gender changers. So if you need to connect two devices that are very far from each other using 1/4" TRS connectors, and you have TRS to XLR adapters and a bunch of XLR cables lying around, you can effectively make a very long TRS cable.
There are other use cases, but I hope this has been enough of an explanation.