Cells are the base units of organisms, some organisms are unicellular (they only consist of one cell), others, like humans, are multicellular (consist of many cells). In humans, similar cells are grouped together into tissues which perform a particular function, different tissues are joined together into organs to complete a more complicated function, and organs are arrangned into interdependant organ systems which together form an organism.
Cells themselves can be divided into two types, prokaryotic and eukaryotic. Prokaryotes have no nucleus (pro is the ancient Greek for 'before' and karyote for 'nucleus), eukaryotic cells do have a nucleus (eu is ancient Greek for 'true' or 'good'). There are other differences between prokaryotes and eukaryotes as well, such as eukaryotes are much bigger, have membrane bound organelles and linear DNA, prokaryotes are smaller, they don't have membrane bound organelles and their DNA is circular (and not contained in a nucleus).
Organelles. Eukaryotic cells contain membrane bound organelles, such and a nucleus and mitochondria (singular = mitochondrion. You need to know what some of these organelles look like and what their function is.
Mitochondria. These are the energy producers of the cell, they produce ATP, which is used by cells to release energy. They have a double membrane, the one on the insided is folded to provide a large surface area.