Herbs can influence digestion in several ways. Many culinary herbs we use today are thought of as adding flavor but their original inclusion was due to their affect on digestion.
The use of herbs in cooking is usually due to what is termed a carminative effect that their volatile oils have. Volatile, or essential oils is what give these herbs their flavor and aroma. Carminatives tend to stimulate digestion and dispel gas, and some can even relieve spasms. Common carminatives include fennel, dill, ginger, peppermint and cardamom. Many times if these herbs arent used in cooking, they are introduced afterwards as teas or other alcoholic drinks.
Another way herbs influence digestion is through adding the flavor of Bitter. The bitter flavor is often ignored in the U.S. and instead sweet, salty and sour is found. A bitter, as simple as it is, can cause a multitude of effects on the digestive tract, causing a hormonal cascade which results in movement in the digestive tract. Many of the carminative herbs mentioned before are also slightly bitter. Bitters tend to drain and move things out of the digestive tract. as well as stimulating secretions. Common bitters include dark leafy greens, dandelion, artichoke leaf, and Oregon grape or the Southwest alternative to Oregon Grape, Agarita.
Herbs sometimes contain mucilage causing a demulcent effect in the digestive tract. The mucilage is slimy and can act to soothe and coat the stomach and intestines. Mucilage is found in things like flax seeds, marshmallow, and aloe.
Herbs can contain prebiotic and probiotic substances and some can act as antacids. Some can do very specific things or many complex effects throughout the system. How the herbs acts depends on so many different things from quality, to dosage, duration of time the herb is used and the body constitution of the person taking the herbs. Unlike drugs, herbs they are much more personalized in who does best with what for how long. It is also a common belief among herbalists that whole herbs are best, and splitting them into phytochemicals--similiar to drugs only asks for more side effects to occur. The herbs come in a complex package of phytochemicals for a reason and have evolved that way for millenia. If we are lucky we can tap into their offerings, and trigger healing responses or, just better digestion following meals.