How come the CBO reported the Federal Deficit for FY2014 was \$483 Billion when debt went up by \$1.1 trillion? The Monthly Budget Review: Summary for Fiscal Year 2014 states that the deficit was \$483 billion.

Treasury Direct shows Total Public Debt Outstanding increasing over the same period from \$16.7 trillion to \$17.8 trillion.

Why is there such a huge difference in these figures?
First off, you are looking at the wrong column to compare like with like.

Total debt went from \$16.7tr to \$17.8tr but that includes intragovernmental debt.  Changes in this number will net out in the deficit calculation (this is one part of the government lending money to another part).

Secondly, you are starting on the wrong date.  You need to go full year, so start from 30-Sep-2013 and go to 30-Sep-2014 (you would think 1 day wouldn't matter, but a lot happens on that last day of the fiscal year!), so your link should be: Treasury Direct FY 2014

So the real number you expect to see change in line with deficit is the "held by public".

This changed from \$11.976tr to \$12.784tr, an increase of $808bn over the period.

So that leaves a gap of $325bn to be explained.

This can be explained by the fact that various things are considered "off budget" for purposes of calculating the deficit, a small example I can remember is the U.S. Postal Service.  Prior to Obama the Iraq and Afghanistan war were considered "off budget".  I think various overseas aid payments are also off-budget.  Also any loans or asset purchases or financial gains and losses will impact the debt value, but will be treated "off budget".

This "off-budget" idea may seem a little dodgy but it should probably be seen in comparison to corporate accounting.  For corporate accounts you would not expect the income statement and cash flow statement to exactly match.

Doing the Math for 2013

Ok, so this is the best I can find, I'm afraid it is projected for 2014 but it gives you the idea.  We can do the calculation for 2013.

The Budget for Fiscal Year 2015

Go to page 207, then there is a table showing the bits that contribute to the debt change.

If we re-ask your question for 2013 (where we have data), then your links are:
Monthly Budget Review: Summary for Fiscal Year 2014
and
Treasury Direct FY2013

Then we see that the deficit was \$680bn and the public debt changed from \$11,269,585,800,039.32   to \$11,976,279,236,073.83 = \$706.7bn

Now according to the budget tables, we see that Unified Deficit is \$680bn but that there is an additional 22bn of changes in financial assets and liabilities, bringing us up to $702bn.

Not bang on, but probably as close as you are going to get - rounding and different sample dates probably makes the difference.  You can see from the projections for 2014 that there is a much bigger value of \$271bn, which is only (!) \$54bn short of the actual number we are seeing.