Otherwise known as a "push through," a reverse print is when you flip a t-shirt inside out, and print on the inside of the shirt. Some of the ink shows through on the other side, and it results in a natural texture determined by the qualities of the fabric. It's a good method to achieve texture without the use of bitmap textures in Photoshop or Illustrator.
You can achieve different looks, depending on the color and thickness of your t-shirt fabric, the color and type of ink, and also how much squeegee pressure is applied.
These are some Quiksilver tees that I spotted out in the store the other day. Notice how the bottom left design used more ink & squeegee pressure for a different effect than the others. On dark shirts, you will typically need more ink and pressure for your graphic to show through, compared to a light t-shirt.
You can reverse print with waterbase ink or plastisol ink. I've even seen reverse printing done with discharge.
Most often, you will want to use water based ink because it will have a softer feel than plastisol ink. Remember, the ink is printed on the inside of the shirt so a softer print is better!
The Ford Bronco is a graphic I reverse screen printed (hand-pulled) in my studio using plastisol ink on a 100% cotton shirt. You can see that more squeegee pressure was applied at the bottom of the graphic versus the top, resulting in a higher density of ink.
You can also print a reverse print with multiple colors. Here's a three-color 4th of July design we made at O'Neill. Reverse printing is good for graphics that would otherwise be too bold if printed normally. The reverse printing "knocks back" the design a bit and makes it more subtle.
Having a more subtle print is also good with men's floral prints. A t-shirt that would otherwise be more appropriate for a pool party, now is turned into a t-shirt you can wear any day of the week.
Why limit yourself to just printing on the inside of the shirt? This was a two-sided print we did at O'Neill.
The palm leaves were reverse printed. Next, the ink was cured. However, I'm not sure if it was put through a dryer or flash-cured on the press (Either method should work).
After that, the t-shirt was flipped back from being inside out, and then reloaded onto the press. Lastly, the O'Neill letters and frame were screened on top.
If you want to screen print on the inside and the outside of the shirt, it needs to be a design that does not require critical registration. You can see the if the O'Neill letters and frame were to float 1/8" in any direction, it would not ruin the design.