There are 3 main letter forms in America and Europe. Cursive, Serif and Sans Serif. I am sure you are familiar with all 3.
The first, Cursive, (some may call it Script) is a font whose letter forms flow from one to another with a single stroke. The word “cursive” comes from the Latin cursivus, meaning “flowing”. Many of you will remember having penmanship classes in the elementary years and these classes were mostly focused on the cursive form. Some point to the origin of the cursive as to the prevention of ink blots. Back in the day when peoples wrote with a quill and loose ink, it was easier to continue a stroke with out a blot than to form each letter individual, lift the pen tip from paper, coming down to paper once again to form another letter, causing more splotches. Cursive form also developed for speed of note taking or writing letters, most likely the first form of short hand today.
Here are some samples of Cursive form, or Script as many will call it.

The second font letter form would be Serif. From the Wikipedia site I found this, “Serifs are thought to have originated in the Roman alphabet with inscriptional lettering—words carved into stone in Roman antiquity. The explanation proposed by Father Edward Catich in his 1968 book The Origin of the Serif is now broadly but not universally accepted: the Roman letter outlines were first painted onto stone, and the stone carvers followed the brush marks which flared at stroke ends and corners, creating serifs. The origin of the word serif is obscure, but apparently almost as recent as the type style. In The British Standard of the Capital Letters contained in the Roman Alphabet, forming a complete code of systematic rules for a mathematical construction and accurate formation of the same (1813) by William Hollins, it defined surripses, usually pronounced “surriphs”, as “projections” which appear at the tops and bottoms of some letters, the O and Q excepted, at the beginning or end, and sometimes at each, of all.”
Although this history makes sense, I have been under the impression and have been for many years that Serif fonts derive from angels. Seraphim is the highest ranked angel. And since monks were doing most of the scribing for a great many years, they would add wings to their letter forms, hence becoming serifs.
It is also believed that Serif fonts are more legible as the serifs (or "little wings") allow your eye to skim along the top of the font more quickly. The little wing on the top of a lowercase "g" makes it easy to determine it is a "g" rather than an "o" or an "a" without even looking at the descender. If you cover up the bottom half of a line of type, you'll see the top half alone is quite readable. However, if you cover up the top half, it is much harder to read by viewing the bottom half alone. One successful design I have seen which only uses the lower half of the letter forms is the Mesa Grill logo, which interestingly enough, uses a sans-serif font. But, I digress...
Here are a few samples of Serif fonts.

And then we come to Sans Serif. These are fonts that do not have little wings, or serifs. Sans comes from the Latin word “sine”, via the French word sans, meaning “without”. Hence Sans Serif.
It seems that big headlines in ads usually use Sans Serif fonts and also many web pages are in a Sans Serif font. Mostly because the font itself makes a big impression, and the web or monitors are not able to hold such fine details of wings on letter forms without vibration.
Here are a few samples of Sans Serif fonts.
