Hydrophilic means "water loving." Hydrophobic means "water fearing." Recall from your general chemistry, "like dissolves like" with regards to solubility. This means that hydrophobic molecules can be dissolved in hydrophobic solvents, and vice versa. Lipids such as oil and cholesterol are hydrophobic molecules and are thus insoluble in water. A good rule of thumb is that all acids are soluble in water. We know sugar is soluble in water, and starch has a similar molecular structure as sugar; it consists of many sugar molecules in a chain.

A saturated fat contains no double bonds in its fatty acid chain. Just remember that saturated means the fat is saturated with hydrogens. Double bonds eliminate two hydrogen atoms per occurrence, and are present in unsaturated fats.

Phospholipids contain two fatty acid chains bound to a hydrophilic head (usually glycerol). Fats (triglycerides) contain three.  

Body fat, also known as triglycerides or triacylglycerols have three fatty acid chains. These hydrocarbon tails are hydrophobic, and they are each attached to the glycerol head, which is hydrophilic via ester linkages. Adipose tissue is a type of connective tissue that plays a structural and protective role, provides stored energy, and helps regulate body temperature.  

A fat is a lipid with three fatty chains linked by an ester linkage to glycerol.

A fatty acid consists of a hydrocarbon chain (carbons bound to hydrogen), with even numbers of carbons from 4 to 28, and a carboxyl group at one end. A triglyceride consists of three fatty acids with their carboxyl end bound to glycerol via an ester bond.

The heads of phospholipids contain a glycerol group and a phosphate group. Both of these groups contain atoms other than hydrogen and carbon, so they are not hydrocarbons. Since phosphate is negatively charged, and glycerol contains oxygens, this part of the molecule is water soluble. In other words, it is hydrophilic, lipophobic, and polar. 

Phospholipids are arranged in bilayers with the hydrophilic heads of pointing out towards the aqueous solutions inside and outside the cell. The hydrophobic tails point towards each other and are in the interior of the membrane. This unique structure allows cells to be water soluble, yet have a protective membrane that is selectively permeable to small, uncharged, hydrophobic molecules such as gasses and steriod hormones. Micelles are spheres of fatty acids in solution, where their heads are on the surface of the sphere, and their tails aggregate in the center of the sphere, avoiding the aqueous environment. Micelles are usually formed by lipids with single fatty acid tails, not two, as is seen in phospholipids. 

A phospholipid has two fatty acid tails, which consist of hydrocarbons with even numbers of carbons ranging from 4 to 28, and a phosphate group attached to a glycerol head, which is hydrophilic. Monoglycerides contain only one fatty acid chain bound to a glycerol head, and triglycerides contain three fatty acid chains. 

A fat (triglyceride/triacylglycerol) consists of three fatty acids linked to glycerol. A phospholipid consists of two fatty acids and a phosphate group linked to glycerol. Thus removing a fatty acid from a triglyceride and replacing it with a phosphate group will yield a phospholipid. Diglycerides contain similar structures to triglycerides, but only have two fatty acid chains bound to the glycerol head. Steroids are lipids, but do not contain fatty acids. Rather they contain four hydrocarbon rings, and they are all derived from cholesterol. The saturation of a fatty acid refers to the presence of hydrogens anywhere they can potentially be present. A saturated fatty acid is said to be saturated with hydrogens.