Limits:
A useful definition is provided by McGraw Hill: "Two extreme permissible sizes of a part between which the actual size is contained, are called Limits".
Fits:
The relationship between two parts, which are to be assembled, with respect to difference of their sizes, before assembly is called ''Fit'.
It is the general term used to signify the range of tightness or looseness which will result from the application of a specific combination of allowances and tolerances in mating parts [ANSI Y14. 5M-1982].
Tolerance:
The total permissible variation of a size is called ''Tolerance''. It is the difference between maximum and minimum limit of size.
** credits: some definitions taken from ANSI text book.