The full notation is customarily 8va, an abbreviation for Italian "ottava" (octave) with the "8" supplying the "otta-" portion.
Placed above the staff, it means "at the octave higher," and in "formal" notation should be used only above a treble staff.

The notes which are to be "played higher" should, in formal notation, be indicated by a dashed line above them, ending with a vertical "slash." Occasionally you will see the note "loco," which means "in place" at the end of the shifted passage, meaning that you play to notes that follow as written.

The 8va symbol is commonly abreviated as simply 8, but sometimes has an added "a" to be read ottava alta - "at the octave higher."

A similar downward octave shift may be noted as "8va bassa," "8a b," or just as "8" placed below the staff. In "formal" notation, this should be used only below a bass staff. A dashed line below the staff, ending with a vertical "slash" should show which notes are to be "shifted."

You will occasionally see the "8va b" above the staff, when necessary to keep the notation neat - it still means "play an octave lower" (because of the "b") and should only be used on a bass staff in formal notation.

I informal notation (we ain't fussy) an 8 above a staff symbol means play the whole d... thing an octave up, and an 8 below the sign means play it an octave lower. By custom in some places, the 8 may or may not be enclosed in brackets, braces, or parentheses.

Very rarely, you may see a "2" in place of the 8, meaning "shift by an octave."

A two octave shift can be similarly indicated by a "15ma," "15a," or just "15." (It. "quindicessima") Theoretically, you could use "15ma basso" (or "15 b") to indicate "play two octaves lower," but it would be extremely rare. Note that the second octave up or down is the 15th, not the 16th.

In the same places where a "2" replaces the "8" for an octave shift, a "2 Okt" means "15va" or 2 octaves shift.

A similar notation, "coll' 8" has a slightly different meaning. An abbreviation of the Italian "coll'ottava" which is "with the octave," it means play both the note written and the octave above. (By extension, placed below a staff, the note written and the octave below?) You're unlikely to see this one in "folk" or "pop" music, but it could crop up in some (finger picker?) guitar notation.

"Modern" notation, notably jazz, has some variations on these - mostly involving arrows, dots, dashes, and such (incredibly hard to put in html, and fairly rare for most of us).

If you can make a guess, and it sounds good, then it's good notation. If it's not fairly obvious, then it's bad notation.

Dave B - be thankful you're not running into stuff written in tenor cleff. I find it a real b... to read.

Not too useful for the common folkie, but for those into answering questions about the esoteric, Music Notation: A Manual of Modern Practice, by Gardner Read, Taplinger Publishing Co, NY, ISBN 0-8008-5453-5 (2d ed paper) about $25 US. Very thorough, but again - not essential for most.

John