The primary purpose of mitochondria in a eukaryotic organism is to supply energy for the rest of the cell. The mitochondria is where adenosine triphosphate (ATP) molecules are produced and stored; ATP is a result of cellular respiration and requires a food source (either produced via photosynthesis in autotrophic organisms or ingested exteriorly in heterotrophs) to be made. Cells vary on the amount of mitochondria that they have; the average animal cell has more than 1,000 of them.
Chloroplasts are where photosynthesis occurs in autotrophic organisms like plants. Within the chloroplast is chlorophyll, which captures sunlight. Then, with a combination of water and carbon dioxide, the light is converted into glucose, where it is then used by the mitochondria to make ATP molecules (ATP is also produced during photosynthesis within the chloroplast). The chlorophyll in the chloroplast is what gives plants their green color.
The most obvious similarity between mitochondria and chloroplast is that they are involved in fueling the cell because they both produce and store some form of energy. Another similarity is that both mitochondria and chloroplast contain some amount of DNA (though most DNA is found in the cell's nucleus). Importantly, the DNA in mitochondria and chloroplast is not the same as the DNA in the nucleus, and the DNA in the mitochondria and chloroplast is circular in shape, which is the shape of DNA in prokaryotes (single cell organisms without a nucleus). The DNA in the nucleus of a eukaryote is coiled up in the form of a chromosome.
The explanation for the similar DNA structure in mitochondria and chloroplast is explained by the theory of endosymbiosis, which was originally proposed by Lynn Margulis in 1970 in her work "The Origin of Eukaryotic Cells." According to Margulis's theory, the eukaryotic cell came from the joining of symbiotic prokaryotes; effectively, prokaryotic cells joined together and eventually evolved into one cell. This theory explains why the mitochondria and chloroplast still have their own independent DNA because they are remnants of what used to be individual organisms.