Type can be a verb, but as a noun, it refers to the shape and style of lettering when it is created with a machine. When it's done by hand, it is called calligraphy. A font used to refer to a single style of lettering in a single size, but that use has faded now that the digital file which creates a font is so seamlessly capable of many different sizes. On any printed page, the information is usually set out in a prescribed format. If the matter is long, there may be subheads, smaller, mini headlines of one to four words which are interspersed within the body copy, breaking the matter into smaller chunks.
Serifs refer to the little flourishes and tails that traditional typography uses.
In fact, you are probably looking at one right now. Traditional examples include Times and Garamond. Sans Serif typefaces were originally called grotesque typefaces by alarmed typographers because they dispensed with these little flourishes in favour of a cleaner, blockier style, more appropriate to the mechanical nature of the printing press and a stylistic denial of the ornate lettering that was the legacy of handwritten books. It was sort of like what happened to painting after photography came along - new technologies freeing artists to pursue a new way of seeing their art. In recent times, the precision of computers has inspired an even more extreme backlash, and there is a whole new style known as distressed type.