You can change the way letters and objects are stroked. You'll find those settings here:
You'll notice those 6 little boxes next to the stroke weight drop box.
A stroked pen path will show us the effects of the top three options. The first box is the default setting. The line terminates in a "Butt Cap" that ends in a flat line at the last point:
The second option rounds off the end of the line and is appropriately called "Round Cap":
The third option is flat like the "Butt Cap," but the end juts out from the end of the last point. This options is called "Projecting Cap."
The bottom three options are best illustrated with stroked text. The default option is called a "Miter Join."
The second option is called "Round Join." The effect is that all the corners become rounded:
The third option is called a "Bevel Join." The effect is that the corners terminate as angles:
There are many applications for these stroke options. I mostly use different settings to fix text that is exhibiting a weird stroke. For example, suppose you need a huge stroke on some text, but the lines end up looking like this:
A good way to fix this is to change the stroke settings to "Round Join." This is what you end up with:
You could place this behind unstroked text to create a nice stroke effect that doesn't eat into the letters.
Enjoy :)