Graphemes include alphabetic letters, typographic ligatures, Chinese characters, numerical digits, punctuation marks, and other individual symbols of any of the world's writing systems. The separate items on a keyboard all produce graphemes when writing in the appropriate software.
A grapheme may or may not carry meaning by itself, and may or may not correspond to a single phoneme.
A grapheme is an abstract concept. A glyph is a specific shape that represents that grapheme, in a specific typeface. For example, the abstract concept of "the Arabic numeral one" is a grapheme which has different glyphs in different typefaces.