For the adjectival possessive pronouns the term unaccentuated personal pronouns is used. Some grammar books use the term adjectivos posesivos (adjectival possessive pronouns) and pronombres possessivos (possessive pronouns). The following table shows the unaccented personal pronouns.

As you can see the personal pronouns refer to the number, and in the first and second person plural the gender of the object that is owned.

Spanish		English
singular mi casa mi bolígrafo	plural   mis casas   mis bolígrafos	singular   my house   my pen	plural   my houses   my pens
tu casa tu bolígrafo	tus casas   tus bolígrafos	your house   your pen	your houses   your pens
su casa su bolígrafo	sus casas   sus bolígrafos	his house   his pen   her house   her pen	his houses   his pens   her houses   her pens
nuestra casa nuestro bolígrafo	nuestras casas   nuestros bolígrafos	our house   our pen	our houses   our pens
vuestra casa vuestro bolígrafo	vuestras casas   vuestros bolígrafos	your house   your pen	your houses   your pens
su casa su bolígrafo	sus casas   sus bolígrafos	their house   their pen	their houses   their pens

There is no difference between his, her and their. You will find out only from the context, which one is meant. Some more examples:

The accentuated personal pronouns do not describe a noun, but they substitute them fully.

Spanish		English
singular   mía   mío	plural   mías   míos	singular   mine   mine	plural   mine   mine
tuya   tuyo	tuyas   tuyos	yours   yours	yours   yours
suya   suyo	suyas   suyos	his   his   hers   hers	his   his   hers   hers
nuestra   nuestro	nuestras   nuestros	ours   ours	ours   ours
vuestra   vuestro	vuestras   vuestros	yours   yours	yours   yours
suya   suyo	suyas   suyos	theirs   theirs	theirs   theirs

The English does not differentiate in number or in gender using the possessive pronouns. Also the accentuated possessive pronouns have to be in accordance with the owned object in gender and number. Again we can't see a difference between his, hers and theirs.

Additionally there is the possibility that the accentuated possessive pronoun is used together with a noun. In those cases it is put after the noun that is described and not before it. One possibility for this kind of construction is when the noun has an undefined article, meaning that the noun is not defined.

Furthermore the accentuated personal pronoun is used when the phrase includes a noun with a demonstrative pronoun.