The verbal prefix has two effects on the meaning of the sentence. First, if it's attached to the verb stem, it "catches" the focus of the sentence, thus emphasising the action itself. In "A gyerekek befutnak a szobába", the focus is on the verb befutnak, and that gives the sentence a neutral tone.

Second, the verbal prefix gives the sentence a perfective meaning. In English this is sometimes expressed with using a simple tense instead of a progressive tense.

• A gyerekek a szobába futnak be. - The children run into the room. They will actually end up in the room.
• A gyerekek a szobába futnak. - The children are running into the room. At least that's what they've planned to do. They might get held up by a good smell from the kitchen instead, who knows?

Both these sentences, by the way, emphasise the goal of their movement, the room. You can find out where the emphasis lies and what it looks like by replacing the object in front of the verb stem with the respective question word:

• A gyerekek hova futnak (be)? - Where do the children run?
• A szobába. - Into the room.

In case of the prefix attached it becomes a bit more complicated:

• A gyerekek mit csinálnak a szobával? - What are the children doing with the room?
• Befutnak. - They run into it.