quant. 1. A large and indeterminate number of objects:
"There were N bugs in that crock!"
Also used in its original sense of a variable name:
"This crock has N bugs, as N goes to infinity."
(The true number of bugs is always at least N + 1.)
2. A variable whose value is inherited from the current context. For example, when a meal is being ordered at a restaurant, N may be understood to mean however many people there are at the table. From the remark "We'd like to order N wonton soups and a family dinner for N - 1" you can deduce that one person at the table wants to eat only soup, even though you don't know how many people there are (see great-wall).
3. 'Nth': adj. The ordinal counterpart of N, senses #1 and #2.
"Now for the Nth and last time..."
In the specific context "Nth-year grad student", N is generally assumed to be at least 4, and is usually 5 or more (see tenured graduate student).
See also random numbers, two-to-the-n.