James, thank you for your question. I had a similar question from Sheereen click here to see my, and my friends answer.
It is thought that a ‘black hole’ is produced when a rather large star comes to the end of it’s life. It collapses in on itself and forms an object of incredibly concentrated matter. As ‘gravity’ is a property of the quantity of matter (see my answer to Ernie’s question) the collapse causes an immense increase in the gravity from the smaller collapsed star.
It is unlikely that our Sun would end in this way as it is classified as a smallish star. It is likely to become something called a ‘Red Dwarf’ star.
The ‘black hole’ is explained by the fact that this concentration of gravity ‘pulls’ light into it, thus the ‘hole’.
Now if you were close to the collapsed star in your spaceship you would also be pulled into it and unfortunately be added to the mass of the collapsed star. Sorry, you will be crushed.
(slightly revised 20/4/2016)