A signature and a number are two marks made on the sheet, and each records something a collector can hold to. The signature is my approval of the print. The number is its fixed place in an edition. Both are set on the day the edition opens, written into the print rather than promised for later, and they are part of what a collector acquires alongside the work itself.
What the signature records
The signature is approval. It says this print left the atelier finished, checked, and meant to be seen, rather than a stray copy or a test sheet. When I sign an impression, I am approving that the surface holds what the work was made to hold.
What the number records
The number records place and total. The fraction tells a collector two facts: how many prints of this work exist, and which one this is. For how the fraction is written and read, see what limited edition means in art.
The total is the part that gives the number its weight. A limited edition is produced in a set quantity or within a set time, then closed once those terms are met. I publish the edition size when the work is released, so the count is on record from the start and fixed, not adjusted later. A number means something only when the total behind it is fixed and declared. A print sold as "limited" with no stated edition size has a number that records nothing, because there is nothing limiting the run. For how artist's proofs are counted into the declared total, see what an artist's proof is.
Where the worth is, and where it is not
Put the two marks together and a signed, numbered print is a documented edition: an artist-approved impression holding a known place in a finite, recorded run. That is a matter of provenance, and it stands apart from any forecast of resale price. I state the edition size at release and do not invent a deadline or a scarcity to push a sale. When an edition reaches its terms it closes; the run stops at the stated total and I do not reopen it.
For the wider picture of why an edition is worth collecting at all, there is a companion answer on edition value. A signed and numbered print carries a documented record: an approved impression holding a known place in a finite run, with the edition terms set at release.