The speed of a film is officially defined in terms of how much exposure will give a certain amount of density (above the density of the film base itself and the inevitable fog level). Increasing development time will give some increase in density in the less exposed parts, which is effectively the same as a higher film speed.
Except that increased development will normally give high contrast - so a speed increasing developer needs to have some means of controlling the contrast.
Film speeds are determined with a standard developer, temperature, time and agitation to give a level playing field. Which also means that your own backyard playing field which may not be as flat as a mill pond (in plainer language, your possibly inaccurate thermometer, timing method (start when you pour in or when you've finished pouring etc.) and agitation will give a different result - and hence film speed.
