Alright, I'm only an amateur linguist, but seeing as it's a fairly basic principle, here goes nothing.

An analytical language is one in which word order has a tremendous effect on meaning, as opposed to a synthetic language, which uses conjugations and other affixes to change meaning and denote the syntactic structure of a sentence.

To compare an analytic language to a synthetic, consider the following sentences in English, an analytic, and Latin, a synthetic.

The dog bites the man.

Canis mordet hominem.

However, if we were to change the word order:

Hominem mordet canis.

The man bites the dog.

The meaning of the sentence in Latin is very nearly the same, if a tad awkward, while in English we are left with a completely different meaning.

This is because Latin uses suffixes to denote parts of a sentence. Canis is the nominative case of the noun canis; while hominem is the accusative case of the noun homo. In other words, canis is doing the acting in the sentence, while homo is being acted upon, requiring a separate conjugation hominem.

In English, however, sentence structure and meaning depends on word placement, as demonstrated above. English lacks separate noun conjugations for each case and instead uses a subject-verb-object(SVO) structure.

Furthermore, topic and emphasis can be changed by changing word order. For example, "I met Mary at the park" can be changed to "In the park, I met Mary." While having the same basic meaning, the corresponding semantic change shifts emphasis from the object, "Mary," to location, "the park."

Other examples of analytical languages include Chinese, which is almost completely analytical, and Thai and Vietnamese.

Sources: Wikipedia, Webster, Latin Made Simple for some quick examples, and my Italian teacher.

Thanks go to wordnerd and Albert Herring for pointing out my woeful linguistic inadequacies.