Titration is the amount of substance. Remembering the "quant"itative is "quantity" and equals "how much", we use titrations to measure the amount of substance present in a specimen. In my field, we titrate antibodies. The best way to explain this is to image you have 5 test tubes. In the first test tube, you place 0.5 ml of pure substance (let's say salt). In the next 4 tubes, you place a given amount of water (0.5 ml). In tube 2, you would place 0.5ml of salt solution into tube 2 and mix - then carry 0.5 of tube 2 substance to tube 3 - then mix and carry to tube 4, then mix and carry to tube 5, then mix and THROW AWAY the 0.5 ml. You have diluted the substance by cutting it in half each time. This carries on until you reach the last positive tube. Eventually (and it might take several tubes) you will achieve a zero substance because you have diluted out the salt.
If you reverse the process, it is considered qualitative. You are starting with a given solution that is going to be positive. In tube 1, remember tha you had salt - you know there is salt so it is positive, but do you know how much? Technically, you do, because you put it there, but if you were making the experiment for someone else, it would only be "positive".
So reverse is qualititative and curve is quantitative.
Both of these methods (using a titration curve and back titration) are quantitative. You are measuring an amount (volume required to reach the end point in this case) and then this allows you to calculate the actual amount/concentration of a substance that is present. The only difference is that in back titration some extra math is required to figure out the amount/concentration of analyte present.