I want to point out since many native speakers here are pointing out this is a matter of perfective vs imperfective. It is NOT. Biegnąć and biegać are BOTH IMPERFECTIVE verbs; they differ in the sense of being indeterminate(habitual, repetitive eg. I run everyday/rarely/sometimes) and determinate (action in progress eg. I am -ing (at the moment): this is never expressed in simple present tense in English such as "I run") aspects. So biegać is an indeterminate imperfective verb and biegnąć is a determinate imperfective verb. I would LOVE to even make the grammar notes on this chapter; it just saddens me that this part of the grammar(which I admit is difficult) is not explained at all here.....
I wasn't even aware that "biegnąć" is a word o.O It turns out that it is correct. Still, "biec" is definitely more used.
And thank you Zkamin for pointing out that I was too careless when writing my answers - you are right, both are imperfective. And the rest of your comment is of course correct as well. I'll edit my comments now where it's applicable.
Seems that we really will have to pay attention to this when doing the T&N for this part of grammar when we'll get to this moment while creating Tree 2.0...
'Gdzie?' means static status or description of a general place, for example: you can ask 'gdzie biegniesz?' but the answer should be: on the road, in the park, in Poland, in the forest. 'Dokad biegniesz?' means where to? - status is mobile, it is the description of the motion. The answer then will be:To school, to the bus station, to somewhere. It is often used in not a proper way even by Poles. So everytime you want to ask about the aim of the motion you should ask: dokąd? (Dokąd biegniesz? Dokąd idziesz?) If you ask about the circumstances, or static (place of beeing of someone or something) you should ask: gdzie? (gdzie to leży?, gdzie jesteś?)
One small tip: what is in English referred to as perfective/imperfective, is in fact named in Polish dokonany/niedokonany - which I would literally translate as accomplished/not accomplished. That already says a lot, although of course there are more nuances.
(This comment was written when I mistakenly mentioned 'imperfective' when it should have been 'indeterminate', so note that doesn't really apply to the topic.)
It is supposed to mean "Where are you running to", but it only works in colloquial language. Technically, it's incorrect - it's just something that people say often, but it's wrong. The right question-word should be "dokąd", but it was forgotten by the course creators, it's not taught in the current version of the course, and therefore it can only be an accepted answer, we cannot change the default one.
As "biegniesz" is happening 'right now', it is very hard to imagine this sentence as "In which place are you running", although it's not impossible. My idea is that it could be used for "In which of the organized running competitions are you taking part?" ;) But really, that's not very probable.
I mean... you can call someone on the phone and they can answer "Oh, I am running at the moment", and you can ask "Oh, where are you running, the XYZ Park or ABC Park", true. But in Polish, I would still use "biegać", which technically corresponds to English Present Simple, but unless you specify the destination, as long as it's just 'running around the park', it's still the right choice.