What does the "della" in the sentence "Vorrei dell'uva" mean? I checked it with the following website: http://www.analisi-grammaticale.biz and the result was, that it stands for an "articolo indeterminativo". But wouldn't that be "una" in this case?
"Della", as other people told in their comments, is an "articolo partitivo", that is a composition of a preposizione (usually: "di") and a articolo determinativo (for example "il", "lo", "la"). As an example:
- di + il = del (vorrei del pane)
- di + lo = dello (vorrei dello zucchero)
- di + la = della (ho comprato della carne)
It is used when you are addressing something whose quantity is not exactly defined. As in the example of yours (vorrei dell'uva), you are not specifing the quantity of grapes that you want: you can have three grapes, or maybe five, or even ten: you just want some. This concept is even more evident when you talk about sugar, or water: you hardly ever specify the exact quantity of sugar that you want, nor even the water (you usually ask for some water - dell'acqua - not for 30 cl of water - 30 centilitri d'acqua -!).
There is in fact a reason why the website www.analisi-grammaticale.biz is classifying 'della' as an indefinite article. Coming to explaining the why in a second, but before that, yes, it is true that articles like 'della' are classified as articoli partitivi, as was already answered, in the 'classical' grammar (the one that, for Italian at least, is derived form Latin and that most of lower grade students study at school).
Now the explanation. In modern grammar, the article has the function of determinator, specifying whether the noun is denoting a specific item that is known to the speaker and to the listener, like in 'I have seen THE cat in the garden', or a generic item, like 'I have seen A cat in the garden'. Now, Italian uses 'uno, una' as English uses 'a'. But Italian, in classical grammar, does not have a plural for the indefinite article. What would you say if you have seen a number of unknown cats in the garden? In Spanish, for example, you could say 'unos gatos', but in Italian 'uno' also means the number one, so it would sound very strange to make it plural, one way or the other. In such a sentence Italian uses 'dei, delle': '(io) ho visto dei gatti nel giardino' which literally translates to 'I have seen some cats in the garden'. Classical grammar introduces the concept of articolo partitivo to classify 'del', the singular form, which also has masculine and feminine genders, and singular and plural. Many believe that this articolo partitivo is artificial as it is not clear what new function it serves in the speech. The school text books often say it is partitivo as it is extracting (parting) a number of generic cats out of the class of all cats. But this is precisely the function of an indefinite article! By this logic, also 'un' should be considered an articolo partitivo, as also 'un' extracts a generic cat out of the class of all cats. This reasoning applies both to countable and uncountable nouns (cats are countable, sugar, rice and many others are uncountable): you can ask for THE sugar, for example at breakfast, while at the grocery you will likely ask for SOME sugar.
Also, some grammar text books go on saying that 'del' is composed by the preposition 'di' and the indefinite article 'il', and similarly for the other forms (della, dei, delle)... Although this might be true from an evolutionary point of view, unfortunately this explanation is more confusing than else, as it generates confusion with a different meaning of 'del' as composed by 'di' and 'il'. Consider the sentence 'il gatto del vicino' or, 'il gatto di+il vicino', that is 'the cat owned by the neighbour': the neighbour is not indeterminate here, and 'del' is in fact introducing a complement.
In conclusion, all this rather confused situation is much semplified if you consider 'del' and its feminine and plural forms as indefinite articles, as is done in the website.
about the evolution and synchronic profile of indefinite articles: chapter 4, Indefinite Articles, in Cognitive Foundations of Grammar, Oxford University Press 1997, Bernd Heine Professor of Linguistics, Institute of African Studies University of Cologne
about the use of partitive articles for plural indefinite articles: http://www.cyberitalian.com/en/html/gra_na.html http://italian.about.com/od/grammar/a/italian-indefinite-article-forms.htm
about the use of partitive articles as determiner: http://mylanguages.org/italian_articles.php
exercise about changing singular indefinite into plural indefinite: http://italian.tolearnfree.com/free-italian-lessons/free-italian-exercise-78095.php