Question: I’ve almost never encountered the word *einfallen* before, so it’s no wonder I don’t understand its meaning in the sentence:

> 
> Mir fällt die Telefonnummer einfach nicht ein.
> 
> 
> 

Dictionaries do everything they can to make the meaning of the sentence yet even more obscure, supplying me with translations like:

> 
> The telephone number doesn’t occur to me easily.  
> 
>  The telphone number doesn’t come to me easily (Probably in the sense of *sich erinnern an*).  
> 
>  The telephone number doesn’t collapse/invade (and does all other things, it's famous for)
> 
> 
>

Answer: 
It can be translated to "remember" or "recall". 

> 
> I just cannot remember the phone number.
> 
> 
> 

So in this case it means the same as *erinnern an*.

Edit: Just for fun: 
In a completely different and somewhat special context, "einfallen" can also have the meaning of "invade". 

Edit2: Changed "telephone" to "phone" in the example sentence to make the sentence sound more like something a British person would say.
I would translate "einfallen" as "come to mind," or to remember.

The literal translation is to "fall into."

But a thought has to "fall into" something.

That "something" is one's mind.