Difference between serif and sans serif

Serifs are small decorative flourishes on the ends of some of the strokes that make up letters and symbols. An example would be the Times New Roman font. Sans serif does not have these details or flourishes. An example would be the Arial font.

Serifs are the usually perpendicular projections found on the termini/endpoints in type. For instance, a capital "I" is usually rendered with 2 crossbars. Those are serifs.

Sans-serif just means "without serif." The definition of serif / sans-serif typefaces should be self-explanatory.

Another name for serif is "roman"; likewise, sans-serif typefaces may also be referred to as grotesque /grotesk or gothic.

There are also different types of serif, such as slab serif—also referred to as Egyptian, mechanistic, orsquare serif—versus bracketed serifs.

Additionally, there are some typefaces with serifs that are still considered sans-serif. Bell Gothic is an example of this. And, lastly, some typefaces have what are called petit-serifs ("small serifs") or semi-serifs.

Serif font:
A serif is the line that trails off a letter shape. The most common serif typefaces are Times New Roman, Baskerville, Caslon, Garamond and Bodini, and there are plenty more. Serif fonts have always been seen as more of a traditional typeface. There are ongoing debates as to whether serif or sans serif is easier on the eye to read. 

San Serif font:
Once you understand what a Serif is, its easy to explain a San Serif, without the trailing lines. Popular san serifs include Helvetica, Arial, Geneva, Tahoma and Veranda. San serif fonts are used widely on the internet. They are considered as more contemporary than the Serif font. 

Slab Serif font:
Although Serif and San Serif are the main types there are others included Slab Serif. This is a font with a thick bold serif. Rockwell is the best known Slab Serif although typewriter style fonts are also slab serif like Courier and American Typewriter. Urban brands like 'the cowshed' have brought back the use of typewriter style fonts.

Legibility vs. readability

Legibility is concerned with the very fine details of typeface design, and in an operational context this usually means the ability to recognise individual letters or words. Readability however concerns the optimum arrangement and layout of whole bodies of text:

An illegible type, set it how you will, cannot be made readable. But the most legible of types can be made unreadable if it is set to too wide a measure, or in too large or too small a size for a particular purpose.(Dowding 1957, p.5; in Lund, 1999 )

Point size

Point size is perhaps the element most used to describe the legibility of a type face, but it can also be the most deceptive. Point size is a legacy from the letterpress system, where each letter is held on a small metal block. The point size actually refers to the size of this metal block, and not the actual size of the letter. The letter does not have to take up the full area of the block face, so two fonts with the same nominal point size can quite easily have different actual sizes. ( Bix, 2002)

X-height

X-height refers to the height of the lower case “x” in a typeface. It is often a better indicator of the apparent size of a typeface than point size ( Poulton, 1972 ; Bix, 2002 ).

Counters

Counters are the “negative spaces” inside a character. They are also good indicators of the actual size of the type.