Agreement means that two or more words must correspond with each other in order to make proper sense of a sentence.
For example, the gender and number of a pronoun or possessive adjective must match the gender and number of the noun it refers to. If you wish to say that a man wants to wear a new shirt he just bought, you would say the following.
John is putting on his new shirt. (masculine singular subject / masculine singular adjective)
That meaning is lost if you change the gender or number of either the subject or the possessive adjective.
Mary is putting on his new shirt.
John is putting on our new shirt.
The boys are putting on my new shirt.
The rules of agreement do not mean that these three examples are incorrect— they could be. But in this case, they are not, because the desired meaning is that a man wants to wear a new shirt he just bought: “He puts on his own shirt.”