MacroQuest2 (MQ2) is a third party software that allows you to send commands from one of your EverQuest clients to other clients. It can be used to send command to your party to follow you, or attack a target or sit and med up.
E3 is, in simple words, a sophisticated macro that uses MQ2 and allows you to configure what spells and abilities your characters should use. So instead of using a regular MQ2 command to order one of your party members to cast a heal, you can configure that party member and tell it whom they should heal, at what health percentage and with which spell.
E3N or E3 Next is a newer version of E3. There is a EQ Might specific version available which is provided by the community (i.e. by Riker and Rekka). You can find the latest version in our discord channel mq2-e3-general.