The relationship between words and meanings is extremely complicated, and belongs to the field of semantics. For now, though, what you need to know is that words do not have single, simple meanings. Traditionally, grammarians have referred to the meanings of words in two parts:
a literal meaning of the word
an association (emotional or otherwise) which the word evokes
For example, both "woman" and "chick" have the denotation "adult female" in North American society, but "chick" has somewhat negative connotations, while "woman" is neutral.
For another example of connotations, consider the following:
There are over 2,000 vagrants in the city.
There are over 2,000 people with no fixed address in the city.
There are over 2,000 homeless in the city.
All three of these expressions refer to exactly the same people, but they will invoke different associations in the reader's mind: a "vagrant" is a public nuisance while a "homeless" person is a worthy object of pity and charity. Presumably, someone writing an editorial in support of a new shelter would use the positive form, while someone writing an editorial in support of anti-loitering laws would use the negative form.
In this case, the dry legal expression "with no fixed address" quite deliberately avoids most of the positive or negative associations of the other two terms -- a legal specialist will try to avoid connotative language altogether when writing legislation, often resorting to archaic Latin or French terms which are not a part of ordinary spoken English, and thus, relatively free of strong emotional associations.
Many of the most obvious changes in the English language over the past few decades have had to do with the connotations of words which refer to groups of people. Since the 1950's, words like "Negro" and "crippled" have acquired strong negative connotations, and have been replaced either by words with neutral connotations (ie "black," "handicapped") or by words with deliberately positive connotations (ie "African-Canadian," "differently-abled").