Live rock refers to rock covered with living plants and animals that has been taken from the ocean and is an important part of the set-up in your seahorse tank. It provides a nesting ground for the necessary bacteria that should exist in your aquarium. It also provides a natural filtration system that helps keep nitrate levels under control.
Sometimes live rock can contain unwanted threats to your seahorses, such as crabs, fireworms and mantis shrimp, but if the rock is treated with fenbendazole this will kill shrimp, anemonae and crabs without harming the smaller crustaceans which are beneficial. An alternative method of ridding your living rock of nasties is to place it in a hypersaline bath - the change in salinity of the water will drive out the invertebrates after which you can lift the rock out and discard the pests. This method does not harm the sessile life or encrusting organisms which you should keep.
Tonga branch live rock (pictured above) is a great double-use addition to your seahorse aquarium. Not only does it provide hitching posts for your seahorses, it is a necessary part of the ecosystem you need to set up in your tank.
You should aim to add around a pound of live rock per gallon to your seahorse tank.
If you're very concerned about adding pests to your aquarium, an alternative method is to start with dry rock which has the advantage of having no harmful organisms present (and is much cheaper to buy than live rock). However, this type of rock will mean your initial cycling of your tank will take much longer since you need to seed the tank with nitrifying bacteria.
Below is a YouTube video of a saltwater fish and live rock tank - although it's not a seahorse tank you can see some examples of branching live rock on the left of the tank: