Quick explanation:
The possessive adjectives in English are: my, your, his, her, our, their. They show possession. The Spanish possessive adjectives are:

mi	my	(singular)
mis	my	(plural)
tu	your	(singular)
tus	your	(plural, familiar)
su	his, her	(singular)
sus	his, her	(plural)
su	their, your	(singular)
sus	their, your	(plural)
nuestro(a)	our	(singular)
nuestros(as)	our	(plural)
vuestro(a)	your	(singular)
vuestros(as)	your	(plural, familiar)

Long Explanation:
A possessive adjective accompanies a noun.

mi embarque - my shipment
tu beneficio - your benefit
nuestro arreglo - our arrangement
su sinceridad - his, her, their or your sincerity
su padre - his, her, their or your father
sus padres - his, her, their or your parents
sus fondos - his, her, their or your money

The Spanish possessive adjective must agree with the number of items a person has.

mi libro - my book
mis libros - my two books

The nosotros and vosotros forms change in gender as well;.

nuestro libro - our book
nuestra mesa - our desk

nuestras familias - our families
nuestros refrescos - our soft drinks

Possessive adjectives can be divided into two groups: the non-stressed and the stressed forms.

The non-stressed possessives are only used in front of nouns. The forms are:

 
mi(s)      nuestro(s)
tu(s)      vuestro(s)
su(s)      su(s)

They must agree in number (and in gender for nuestro and vuestro) with the noun, not the person or pronoun to which the refer:

• mis libros
• nuestra madre

Remember that su(s) is ambiguous; su casa = your [usted] house, his house, her house, its house, your [ustedes] house, their [male and/or female] house.

• A mi gato no le gustan tus perros.
  My cat doesn't like your dogs.
• Sus caballos arruinaron nuestras flores.
  Your [formal] / his / her / their horses ruined our flowers.

The stressed possessives are:

mío       nuestro
tuyo      vuestro
suyo      suyo

They are used after nouns, or can be used with articles as pronouns:

• Ésa es la casa mía.
  That is my house. [Or: That's the house that belongs to me.]
• Esa casa mía.
  That house of mine.
• Mi casa es más grande que la tuya.
  My house is larger than yours.

Note that the forms su and suyo are ambiguous and for clarity or emphasis sake may be replaced by the expressions de usted, de él, de ella, de ustedes, de ellas, and de ellos. For example:

• La casa de él es roja, pero la de ella es blanca.
  His house is red, but hers is white.
• (Su casa es roja pero la suya es blanca.)
  (Virtually meaningless.)