Organelle is the term used to describe membrane--bound structures within eukaryotic cells that perform specific functions. Most of a cell's organelles are located between the cell's nucleus(also an organelle) which contains its DNA and its cell membrane--a selectively permeable organelle involved in transport. They are found in the cytoplasm--the liquid portion of a cell.
Mitochondria are organelles where respiration occurs. Ribosomes are tiny factories for protein synthesis. Centrioles in animal cells are organelles that are involved in the formation of the spindle during cell division. Vacuoles which are smaller in animal cells in comparison to plant cells are organelles for storage. Endoplasmic reticulum are microtubules used for transport of materials inside cells and also for producing chemical compounds such as carbohydrates and lipids in the smooth ER and proteins in the rough ER which has ribosomes attached to it. Tiny ribosomes engage in protein synthesis and are also found free-floating in the cytoplasm.The golgi apparatus are where cell secretions are packaged and modified. There are chloroplasts in plant cells and algae which are the sites of photosynthesis. Plant cells contain cell walls which give support and structure to the plant cell.
These are a few examples of the numerous organelles, vital components of eukaryotic cells.