Put simply, photosynthesis is a process that plants undergo where they take light energy from the sun and convert it into chemical energy and chlorophyll. As with plants, algae also photosynthesizes. Plants and algae use the chemical energy that they produce during the process as "food" to keep themselves alive. This means that both plants and algae are autotrophic, which means "self-feeding."
When considering the habitats of plants and of algae, you will note both similarities and differences. Both plants and algae can grow in water, so this is a characteristic they share. However, algae grows exclusively in water, whereas plants grow either in the soil or in water, depending on their variety. When both plants and algae are growing in the same body of water, they will have to compete for light and resources.
There are some shared characteristics between algae and plants in their uses and functions. Both algae and plants exist, in part, to be eaten by living creatures. These creatures may, in turn, end up being food for a larger animal. As such, plants and algae are essential parts of an ecosystem. However, both plants and algae can become a threat to the diversity of that ecosystem if they become too numerous and start to wipe out the competition.
Other characteristics that plants share with algae relate to reproduction. Plants and some varieties of algae perform meiosis, which is a division of the reproductive cells, to ensure genetic diversity. They also both produce male and female gametes in order to fertilize themselves or other similar organisms nearby. However, one difference is that some single-celled algae reproduces by mitosis, or asexual reproduction.