Question: I'm a bit confused as to why the inifinive form of "danser" is used in the phrase from the title.

I'd imagine that "Je regarde Anna danse" would be correct, as Anna is performing the action of the very and thus I would conjugate the verb to show that. Obviously this is incorrect, but could someone explain why?

Answer: 
> 
> Je regarde Anna danser. 
> 
> 
> 

*Je regarde* = proposition principale 

*Anna danser* = proposition infinitive

In this type of sentences the verb in *la proposition principale* is usually a verb of perception (regarder, voir, entendre, écouter...). Both the proposition principale and the proposition infinitive contain a subject (*je*, *Anna*) and a verb (*regarde*, *danser*). Other examples of such constructions could be: *J'entends le train siffler. Nous regardons les avions s'éloigner dans la nuit.* 

You're right that \* *Je regarde Anna danse* is incorrect, however it is possible to say: 

> 
> Je regarde Anna qui danse.
> 
> 
> 

What is then the difference between *Je regarde Anna danser* and *Je regarde Anna qui danse*? 
The first sentence emphasizes the action (dancing), while the second one emphasizes the actor (Anna).
Deux verbes se suivent, le deuxième se met à l'infinitif.