In physics, energy is described as a quantification of the ability to do work. This is no different in Minecraft, as various different forms of energy are required to power the many different machines available in the Technic Pack.
There are seven main types of Energy in the Technic Pack with major mods dedicated to the first three.
Minecraft Joules or MJ are used to power BuildCraft machines.
Energy Units or EU are used to power IndustrialCraft machines.
Vis and Taint are used to power ThaumCraft machines.
Heat is used to power many things in Vanilla Minecraft as well as many of the mods in the Technic Pack.
Note that the Laws of Thermodynamics do not apply in the Minecraft or Technic Pack world, so creating many otherwise impossible contraptions is quite possible. Examples include Free-Energy Machines and Perpetual Motion Machines.
Minecraft Joules are generated from the four types of Engines from Buildcraft and from Energy Links.
Converts Redstone energy into Minecraft Joules.
Converts Heat into Minecraft Joules.
Heat is generated using various types of fuel such as Coal or Wood.
Takes in Oil or Buildcraft Fuel and outputs Minecraft Joules.
Takes in EU and outputs Minecraft Joules. Works just like a normal buildcraft engine.
An EU or Energy Unit is a measure of energy production, consumption, transmission and storage.
These units are not similar to IRL electricity, basically these are virtual "items", that can stack unlimited amount of times and needs storage items like RE Battery or transportation\distribution network to be used. EU stored in items or devices won't decay over time.
Every Industrial Craft 2 machine is involved in the production or consumption of EU.
EU is not related to Redstone current, but multiple machines can be affected by redstone currents, and a Detector Cable produces redstone current if there is any EU passing through it. Some machines allow a lever to be mounted directly on its block.
Raw EU values are used to measure capacity of energy storage items or blocks.
IndustrialCraft provides a number of different sources of EU.
Generator - Converts Heat to EUs. Heat is generated using various types of fuel such as Coal or Wood.
Solar Panel - Generates EU over time during the day.
Geothermal Generator - Takes in Lava and outputs EU.
Water Mill - Takes in Water and outputs EU.
Wind Mill - Generates EU over time depending on height and other variables.
Nuclear Reactor - Converts Refined Uranium to EU.
EU/t means Energy units per tick. If the computer or server is able to handle all ingame calculations, the game will operate at about 20 ticks per second. If this is not the case, the clockrate will drop significantly and you will notice ingame time slowdown. If the clockrate is 10, a second in game will last as long as 2 IRL seconds.
In order to measure the amount of EU being created by one of the generators, consumed by one of the other machines, or the amount of EU passing through a cable, you must use an EU Reader. In order to use this you must right click on the block, wait for a few seconds, and right click on it again. It will then come up with the average EU/t in that block.
EU-Packet / VoltageEdit
EU-Packets are the transmission containers of EUs. They represent voltage in Industrial Craft 2. This value has nothing with IRL voltage.
EU-Packets come in different sizes ranging from 1 EU to 2048 EU, unlike IC1 you may not change the EU output of storage devices.
There is no way to measure what size of packets travels through a cable or machine but they can be read from EU emitting blocks.
Emitters such as generators, storage units, and transformers can emit EU-Packets.
Cables can carry unlimited amounts of EU, but only EU-Packets that are the same or below of their maximum voltage. You can send unlimited amounts of 32 EU-Packets through a Copper cable but not a single 128 EU-Packet. The clue is that energy loss of a cable isn't connected to the total amount of EU/t but to every single packet. So sending 100 32 EU-Packets results in 100 times the energy loss of the cable where sending one 2048 EU-Packet only result in one time the energy loss of the cable. More on that in Voltage Efficiency.
Bluelectricity is from the redpower mod and is generated by either Solar Panels (redpower ones) or Thermopiles. This powers machines from the Redpower mod such as frame motors and blulectric alloy furnaces.
Thaumcraft introduces Vis. It's essentially an ambient "natural" magical radiation that can be found in the environment itself. It can be gathered in liquid form by, amongother things, dropping various items into a Crucible. Once gathered, it's used in a manner similar to EU or MJ by various Thaumcraft Machines. This is noteworthy primarily because Thaumcraft has a converter that takes this liquid "Thaum" and produces either MJ or EU for Buildcraft and Industrialcraft machines respectively. It's certainly not an overt or easily obtainable energy source.
Heat is generated by burning certain materials in the Minecraft world including Saplings, Sticks, Wooden Planks, Wood, Charcol, Coal, Fences, Buckets of Lava, etc.
Using Power Crystal's Power Converters Mod it is possible to convert between the various types of Energy in the Technic Pack. This allows for much more flexibility in design allowing you to, for example, power a Buildcraft machine with EUs.