"I am running very fast."
Translation:Я бегу очень быстро.
Many verbs denoting movement come in pairs: бежать - бегать, идти - ходить, плыть - плавать, etc. The first verb in each pair is called 'directed', and the second one 'undirected'. Directed verbs are used when a specific movement (in a specific direction) is described; undirected verbs are used when a general movement, or a movement in multiple directions or without a specific direction is described. So, Я бегу очень быстро (directed verb) = I am running very fast. Я бегаю очень быстро (undirected verb) = I run very fast.
Directed verbs usually correspond to a continuous tense. Here are some examples:
Птицы летают - Birds fly. (A general statement, without referring to a specific movement - undirected verb).
Птицы летают по небу - Birds are flying in the sky. (Concrete movement, but in multiple directions - undirected verb)
Птицы летят на юг - Birds are flying to the south. (Concrete movement in a specific direction - directed verb).
Я иду на работу. - I am going to work. (Specific movement in a specific direction - directed verb).
Я хожу на работу каждый день. - I go to work every day. (Repeating movement - undirected verb.)
Я хожу туда-сюда. - I am walking back-and-forth. (Movement in two directions - undirected verb).
Source (PDF, in Russian).
Бегу́ is a normal imperfective ('I'm running', now), бе́гаю is a frequentative (running more than 1 time, running to different places, running in general). It's similar to the difference between иду́ and хожу́, or е́ду and е́зжу.