Translation:She bored us all evening with her photos of the party.
There is often a 'la' in esperanto when there does not need to be one in the english for it to make sense, comes up a lot in time and also with things like Malfermu la buŝon (open your mouth) or li parolas la anglan ( he speaks english). It is just the way the language is, you get used to it.
Consider these two sentences
La tuta vespero estis bela
Mi ludis la tutan vesperon
The former 'The whole night' is a static subject that is not a measure of a period of time but rather a singular item.
The latter 'the whole night' is a dynamic measure of time that includes 'many moments'. The accusative is saying 'throughout the whole night' instead of talking about the night as a noun.
In short accusative time is experiencing 'through' the time, and non-accusative time is the whole time frame as a noun.