And I thought further would be my easiest subject....boy was I wrong
Discrete:If we're given shoe sizes like 6, 6.5, 7, 7.5, 8, 8.5, 9 and so on... This is discrete data as our shoe sizes can only take these values (they cannot be in between).
All of the data in this table here is discrete:
http://www.zangle.com.au/wp-content/uploads/2012/05/womanssizeshoes3.png (some quick googling)
Continuous:If we were to measure our shoes to see their physical length in centimetres, this would be continuous. My shoe is not going to be 22.51cm, but rather 22.516367219cm... and so on in decimal places. The number of decimal places is limited by our recording equipment, what we use to measure the length.
Categorical vs Numerical:
The two examples above are numerical pieces of data. As Sense was saying before, if we expressed our shoe size as not a number but as a category (such as small, medium, large, extra large) ... then we'd have categorical data.
Hopefully that helps clear some things up.