What most often appears to be a dirt on a roof is, usually mould and lichen growth. This happens especially in the case of tiled roofs. Both concrete tiles, and terracotta tiles are a haven for the growth of unsightly mold due to, compared with a metal roof, they have a rougher surface. Concrete and terracotta tiles have many "nooks" and "crannies" on their surface where fungus spores get a foothold, and start to grow.
This is not to suggest that metal roofs don't attract mold growth as they can and will. Look particularly in the shaded sections of a metal roof where they are likely to be covered with some kind of fungus. The solution for a dirty roof is Roof Cleaning a process that suits many tile roofs. Depending on the type of roof you have, it's age, and exposure it may be fine to have your roof cleaned. This may involve a simple high pressure water blast. Where fungus spores have a strong foothold, you may need an additional mold killing solution to be applied to the roof before cleaning.
Not all roofs should be pressure cleaned,in particular with concrete tiled roofs, if they are older than approximately 15 years, pressure cleaning it could cause more long-term harm than good. This is because concrete tiles, when they are new have an oxide slurry coating applied to their surface, and then a protective glaze baked over the top.
This protective glaze breaks down over a period of time due to the exposure to the elements (it usually takes between 6 and 10 years), leaving the oxide coat exposed. This oxide coat becomes extremely chalky over time and pressure cleaning your roof removes much of this coating exposure your tiles. This leaves your tiles less protected, and they lose their colour often leaving you with a roof that looks worse than before it was cleaned!
The solution to this is to have your roof sealed and painted after having your roof cleaned. This can restore it to looking like new roof and ad protection to the surface of the tiles, preventing any absorption of water when it rains. With newer roofs, it's normally fine to have them pressure cleaned, and this can greatly improve the appearance of your home.