Basically, after the Romans left Britain in 410 AD, Germanic tribes started to populate Britain. A few of the main tribes were the Anglos, and the Saxons, which gave historians the name Anglo-Saxon. Along with themselves, they brought their vocabulary (Anglo-Saxon words), words like house, send, or stop.
Latinate words come from, you guessed it, Latin. In 591, Christian missionaries brought Latin to Britain, and so from the Latin, many English words were derived. Latinate words have Latin roots, such as, aquarium (aqua in Latin means water).
Now that the little history lesson is taken care of (hopefully I got the facts right, if not let me know!), onto how it matters to you as a writer. Let's start by identifying the different characteristics of each type of word.
-Usually less formal
-Often single syllables
-Can be more forceful, shocking, and harsher. For example, some profanities are of Anglo-Saxon origin.
Some examples of Anglo-Saxon words: send, build, stop, hearty, mock, the s-word, the f-word (I use those short forms to be sensitive.)
-Usually more formal
-Have a more "high society"/proper feel
-Stress is often on the second syllable
-Often turn into euphemisms for blunter Anglo-Saxon words
Some examples of Latinate words (see how they contrast to Anglo-Saxon words): transmit, construct, resist, cordial, imitate, excrement, intercourse
The major thing about knowing about these two types of words is that a writer needs to understand how to use them together. If a writer uses to many Latinate words then that will lead to stuffy prose. On the flip side, if a writer uses too many Anglo-Saxon words it will lead to plain prose. Although, using more Anglo-Saxon words is generally a better idea, it's important to know how to use Latinate words. I find, that the trick to using Latinate words the best way, is to have them contrasting with Anglo-Saxon words. Such as, "The woman was the opposite of stale, and unprofitable." The word 'stale' being the Anglo-Saxon word, and 'unprofitable' being the Latinate word. It's important to use the Latinate words among Anglo-Saxon words to create interesting prose, so long as you don't get carried away with overly formal Latinate words.
Alright, so this post is bordering on confusing, so to sum everything up. It's important to be aware of the different types of words, and the effects they have on your writing. It really is a judgement call as to whether you have too many Latinate words, or not enough in your writing. Good luck!