Yes, the E11 should increase the sound quality in most cases. How much it does depends on your earphones and also your phone though.
Basically, a mp3 music player needs to have both a DAC and and amp to produce sound for your headphones.
A mp3 file is digital, meaning it is all 1's and 0's, as opposed to analog which would be something like a vinyl disk. A DAC is a Digital to Analog converter, meaning that it takes the .mp3 file and converts it to actual sound waves and music. This analog signal is then fed through the amplifier, which boosts the signal and provides power so that your headphones can produce the sound.
There is a DAC and also an amplifier built into your phone as well as pretty much every mp3 player. However, a phone will typically not have a very good amplifier since there isn't too much room to fit one in. Using an external amp will improve the sound quality and will also allow you to provide more power to your headphones since it has its own power source.
A LOD is a Line Out Drive or Dock or something. It basically is a special cable available for certain players that allows you to bypass the built in amp, so that the signal goes directly from the DAC to your own amp. This is good because there's no need to amplify the signal twice and if the internal amp was a really bad one then you can prevent the music from being distorted by skipping past that section and going straight to your own amp.