What does "dirty" mean in relation to a drink?

I saw in a movie a girl asking for a "very dirty" drink. Did she want higher alcohol content?

I searched definitions of dirty but I couldn't find any related to a drink.

Solution 1:

Here is an explanation with some examples:

To make a drink “dirty,” means you may slightly change the color and taste by adding or changing some of the essential ingredients. A dirty martini for instance contains olive juice. There are actually several versions of the dirty mojito. One classic is to use raw sugar instead of white granulated. This gives the drink a very slightly tan or “dirty” color.

Solution 2:

A martini is simply gin (or vodka) with some proportion of vermouth (the relative proportion determines whether it is "dry" - almost purely gin or vodka - or "wet" - more vermouth.) It can be garnished with an olive or a lemon twist.

If you garnish with an olive, and then add a bit of the brine from the olive jar to the drink, that is a "dirty martini." A "very dirty" martini would, I'm guessing, contain a lot of brine.