So here are two perfect examples of eukaryotic cells, plant and animal cells and as you can see they contain a nucleus and other organelles surrounded by a membrane. 

It is important to mention that all cells, including eukaryotes are surrounded by a cell membrane. This membrane acts more like a liquid than a solid and is comprised mainly of a phospholipid bilayer that does a great job of lining the cell with a protective layer whose design is selectively permeable. So the layer in the middle (those fatty acid tails) are great at keeping a thin layer of separation between what is in the  cell and its surrounding environment. Additionally embedded in the phospholipid bilayer are two main types proteins. Peripheral proteins (like your peripheral vision) are usually just on one side of the membrane and integral proteins are found on both sides of the membrane layer and typically act as tunnels are shoots for materials to pass through. So certain types of molecules that are polar (like water) or large in size (like glucose) have their own special channel/tunnel that allow them to pass through the membrane via the protein channels.  So just like an organism needs to take in nutrients and get rid of wastes, this needs to happen on a cellular level as well and the design of the cell membrane makes this possible in a very selective manner.

Additionally eukaryotic cells have a cytoplasm. The solid portion allows a cell to hold or change its shape as needed, much like the scaffolding of a building is designed to hold its shape. The other part of the cytoplasm is the fluid like ortion that also holds the organelles in place and acts a a medium for chemical reactions is the cytosol, the liquid-like portion of the cytoplasm. This graphic here is showing the breakdown of where fluids are found in our body, and you can see 67% is intracellular fluid, that’s cytosol in our cells.

Eukaryotic cells have a nucleus. You can see it here stained in blue. That’s all genetic material stored in the nucleus. ANd of course also in the nucleus is the dark spot called the nucleolus, where RNA and ribosomes are created.