Arrowroot is an herb which is often cultivated for the starch that can be derived from its rhizomes (or rootstock). The resulting starch is extremely high in carbohydrates and devoid of nutrients. Like tapioca, though, it is also devoid of anti-nutrients such as gluten and phytates which are a big reason that we avoid grains and legumes. Arrowroot can be used in conjunction with almond flour or coconut flour to make Paleo baked goods light and fluffy. In fact, tapioca is sometimes labeled as arrowroot.
Paleo and Carbohydrates
Because arrowroot is high in carbs and relatively devoid of nutrients, treats made with it are to be limited to rare occasions, rather than a daily occurrence. Those who are very active might find the carb boost that arrowroot provides to be beneficial, but those who are more sedentary or more sensitive to carbs might want to avoid arrowroot altogether. As always, it is a case of N=1. You have to conduct the experiment on yourself because only you can find out what makes you feel and perform your best.
Robb Wolf has a recipe in which he uses arrowroot powder as a thickener and discusses the benefits of using it here.