In 1986 Randell Mills MD developed a theory that hydrogen atoms could shrink, and release lots of energy in the process.
He called the resultant entity a "Hydrino" (little Hydrogen), and started a company called Blacklight Power, Inc. to commercialize his process. He published his theory in a book he wrote, which is available in PDF format on his website. Unfortunately, the book contains so much mathematics that many people won't bother with it.
On this page I will try to present the energy related aspect of his theory in language that I hope will be accessible to many.

According to Dr. Mills, when a hydrogen atom collides with certain other atoms or ions, it can sometimes transfer a quantity of energy to the other atom, and shrink at the same time, becoming a Hydrino in the process. The atom that it collided with is called the "catalyst", because it helps the Hydrino shrink. Once a Hydrino has formed, it can shrink even further through collisions with other catalyst atoms. Each collision potentially resulting in another shrinkage.

Each successive level of shrinkage releases even more energy than the previous level. In other words, the smaller the Hydrino gets, the more energy it releases each time it shrinks another level.

To get an idea of the amounts of energy involved, I now need to introduce the concept of the "electron volt" (eV).
An eV is the amount of energy that a single electron gains when it passes through a voltage drop of one volt.
Since a volt isn't much (a "dry cell" is about 1.5 volts), and the electric charge on an electron is utterly minuscule, an eV is a very tiny amount of energy. Nevertheless, it is a very representative measure of the energy involved in chemical reactions.
e.g. when Hydrogen and Oxygen combine to form a water molecule, about 2.5 eV of energy is released per water molecule formed.

When Hydrogen shrinks to form a second level Hydrino (Hydrogen itself is considered to be the first level Hydrino), about 41 eV of energy is released. This is already about 16 times more than when Hydrogen and Oxygen combine to form water. And it gets better from there. If that newly formed Hydrino collides with another catalyst atom, and shrinks again, to the third level, then an additional 68 eV is released. This can go on for quite a way, and the amount gets bigger each time. Here is a table of some level numbers, and the energy released in dropping to that level from the previous level, IOW when you go from e.g. level 4 to level 5, 122 eV is released. (BTW larger level numbers represent smaller Hydrinos).

41 eV
68 eV
95 eV
122 eV
150 eV
177 eV
204 eV
258 eV

For those of you with a mathematical bent, the formula is ((2 x n) -1) x 13.598 eV, where "n" is the level number.
(BTW the maximum level number is certainly no larger than 137, and may well be less than that, not least because when a Hydrino gets very small, it may undergo fusion reactions with other atoms.)
Of course, the numbers can be added up. IOW if you start with a Hydrogen atom, and end up with e.g. a level 5 Hydrino, then you get a total of 41 + 68 + 95 + 122 = 326 eV.
The total for any level can be calculated with the formula (n^2 -1) x 13.598 eV.

Since 2.5 eV of energy was released when a water molecule was formed, it also takes about that much to split it apart again into H2 and  1/2 O2. However it takes about another 4.5 eV to split the H2 molecule into 2 H atoms, ready to be shrunk into Hydrinos. Now we have used 2.5 + 4.5 = 7 eV. If each Hydrogen atom formed from the H2 now converts to a Hydrino, we get 2 x 41 eV = 82 eV ( > 11 times the energy needed to split the water and H2, and this is just for shrinkage to the second level. Any energy released through further shrinkage is a bonus.)

This means that water could be a fuel, and the oceans are full of it!

There are a few atoms that can be catalysts, however most are ions. An ion is an atom that has lost one or more electrons.
I will indicate this with a "+" for each lost electron, e.g. Ar+ is an atom of Argon that has lost 1 electron.
Some catalysts are (only a few are listed here, there are many more):

Argon ion (Argon is about 1% of the air)
Oxygen ion (lost two electrons)
Potassium atom
Iron atom

You may be wondering about the "m" column in the table. In all of the text above, I have talked about shrinking the Hydrino one level at a time. However some catalysts can shrink it more than one level at a time. This is the "m" (for "multiple") value of the catalyst. e.g. O++ can shrink a Hydrino 2 levels in one collision, say  from level 5 to level 7 directly rather than in two separate hops.
When this happens the energy released is the sum of the differences between the levels, so for this example it is 150 + 177 = 327 eV, in one go (see energy amounts in first table for levels 6 and 7).
Note however that not all collisions result in a shrinkage reaction, in fact almost all don't. Usually, the atoms just bounce off one another. All of the catalysts in the table are very common, and hence cheap. However Oxygen usually likes to grab electrons, and become a negative ion (O--), so making it give up two electrons instead is difficult to do, which means that O++ is only formed at very high temperatures, or where very energetic reactions are taking place (such as where Hydrinos are being formed!).