Algae are any eukaryotes, other than plants, that conduct photosynthesis. They range from single-celled organisms to multicellular seaweeds over 180 feet in length with specialized organs. They are found in most environments, especially very wet ones, perhaps most notably the oceans, where they are the dominant producers.
Algae are an extremely varied group with boundaries as much defined by what they are not as what they are. While plants have several characteristics that distinguish them from algae, the same can not be said of algae in relation to plants. Multicellular algaes, such as kelp, do have distinct structures, such as fronds, floats, and holdfasts, but they do not have well-differentiated tissues, and any part of a kelp organism will, under the right conditions, regrow the rest of its structures.
Algae are vastly important organisms, in many ways more important to life overall than the more commonly encountered plants. They sit at the base of nearly all oceanic food chains, and single-celled algaes such as diatoms are actually produce vastly more oxygen than all land plants combined. Indeed, they produce enough oxygen that, should all land plants disappear, there would still be sufficient atmospheric oxygen produced for many land animals to breathe.