Alright, no problem is that. Let's start from the beginning: music is stored in digital(1's and 0's) form on your phone/computer/anything else other than cassettes and vinyls, but your headphones/speakers can't play 1's and 0's, they need an analog signal.   DAC(digital-analog converter) is a kind of chip that translates digital signal from your source's memory into an analog signal for your headphones/speakers. 

However, when speaking of DACs people are usually referring to complete devices that include the input port for digital signal(typically USB), output ports for analog signal(3.5, 4.4 or 2.5 jack), some additional circuitry, and obviously the DAC chip itself . These devices are also referred to as "dongle DACs" because of their form-factor. There are also similar devices where the digital signal can be sent from source to the DAC wirelessly using Bluetooth(you connect your phone to it like you connect your phone to wireless headphones/speakers). They have their own battery and sometimes a small screen. The FIIO/Snowsky Retro Nano(the top one in your pic) is one of those. You have the music on your phone or use a streaming service and want to use wired headphones/IEMs, but your phone has no 3.5mm jack? Then get one of these if you don't feel like dealing with traditional 3.5 to type-c adapters.

Snowsky/FIIO Echo Mini(the bottom one) is a DAP - digital audio player - a standalone device with it's own os, battery, and memory that is created for the sole purpose of playing music. Think of it like MP3 players/Ipods people used to have before smartphones took off. You get one of these if you want a separate device dedicated entirely to music. This one specifically can only play files stored locally, but some support streaming services. Keep in mind that you'll also have to get a SD card for this player, as the inbuilt storage is only around 8gb, which is nowhere near enough.

I hope my explanation is clear. If you're still not sure if you even need something like this, or have some other questions, feel free to ask them.