While Flinders Petrie was leading excacvations at the cemetery of Naqada, Quibell was working at Ballas. Both numbered graves from 1 onwards. To distinguish Predynastic objects coming from graves at Ballas, from those excavated from Naqda, the letter 'Q' was subsequently added. This vessel is from grave 341 at Ballas, the 'Q' denoting that Quibell was the excavator in charge of fieldwork there. The number below it - 25.95/39 - is the accession number given to this object when it was catalogued by Chadwick Museum in Bolton.
Links
[1] https://egyptartefacts.griffith.ox.ac.uk/excavations/1894-95-el-ballas