I would assume that a weight training "diary" is the same as a training log. It is a form that you can use to fill in your lifting information--the date, how much weight, how many sets, how many reps. You could also indicate what sort and how much cardio you did. In this way, you can track your progress over time.
It would also be useful to indicate other information on it too. For example, how you felt that day --was it easy, could you keep good form, did you enjoy yourself, did you need to pause the vcr and take more rest than Cathe, etc.
Another thing you might want to consider is tracking your diet along with it. Maybe you would notice that if you had a light dinner the previous day that it was difficult to do cardio. Or that if you had a lot of protein one week, that you were stronger the next. (I made that example up, I have no real idea if it would work that way. I suspect it might over the course of a month though.)
Since discovering Cathe, I am more sporadic about keeping one. The form I used was downloadable from the web site below. I recorded my additional info on the back page and kept it all in a 3 ring binder.
http://davedraper.com/training-log-sheet.html
Jeanne