A mortise lock is an older style of lock that is coming back into fashion in America. Most people have a cylindrical lock, where a cylinder is bored into the side of the door and a little material is removed for the plate- it's very possible you've had to install a lock or replace a lock like this one, in your lifetime.
The name of the mortise lock is in reference to a wood joining style, mortise and tenon, where a whole is dug in one piece of wood. This is the mortise. The other piece of wood has a tenon- a bit that is carefully shaped to fit exactly in the mortise. They are joined in 'insert tab a into slot b' style. It's still used in a lot of modern furniture making, typically using glue to secure the join (though there are plenty of methods for securing this type joining, some a great deal more complex).
In the case of the mortise lock, the 'tenon' part is the lock body- that is, the part of the lock that goes into your door. These types of locks require more wood to be dug out of the side of the door than a cylindrical lock. It's the only way to fit the larger lock body into the door. While this can make the body of the door weaker, mortise locks in general are considered stronger than cylinder locks- the lock body is larger and more substantial, and can handle more substantial hardware internally.
Some mortise locks use the typical pin tumbler lock mechanism, but because of the larger lock body, lever lock mechanisms are possible and also widely used. Or, more rarely, warded lock mechanism- though these are an older lock style that are used typically in heritage or low-security applications, as they are vulnerable to being opened with a skeleton key. (If you were ever wondering what type of lock mechanism a skeleton key was used for, it was for warded locks.)
If you decide to install a mortise lock in your home, they can be installed by hand, but it might be worth calling someone who specializes in mortise lock installation. For one thing, a specialist is almost certainly going to have a mortising jig as part of their equipment, thereby rendering what could be the most tedious part of the exercise much easier.
Even if you don't, though, they are very interesting locks and worth learning more about.