Hi Bride to be!
There are so many printing techniques out there, but Letterpress invites are known for it's thickness and tactile luxury. You really need to hold one in your hand to feel the difference between a letterpress invite and a standard digital printed invite, this would also help you understand why they tend to cost alot more than printed invites.
Letterpressing creates an indented, almost "carved-in-look". It is made by taking your designs and making a metal or ploymer plate, a thick paint-like ink is then applied to the plate and then deeply pressed into the super thick card. When you run your hands over it, you will feel the indentation.
Not everyone can letterpress, it requires experience, patience and the right equipment to letterpress, even designing for letterpress is not something every can do.
If you're thinking of letterpress, I would suggest finding a designer who has letterpress experience, and ordering some samples.
Feel free to get in touch anytime, if you need some help with your wedding stationery.
Happy Wedding Planning!