Direct sound is that sound which is directly traveling from the source to the receiving point. Indirect sound means that it is not going directly means say from my mouth to your ear. Say if there is a wall here, indirect sound means which is going bouncing off the wall and then coming to your ear. Direct sound is directly going from my lips to your ear.
Indirect sound and direct sound classification is mainly internal acoustics. A big Hall or maybe in a big home theater it applies. Speaker’s sound before it reaches you gets reflected from the wall. If you have some absorption on wall, it will avoid reflection.
In a home people who are talking to each other is direct sound. There is hardly any indirect sound in a house because it’s such a small room, the reflections are very closely spaced you don’t really hear it.
If you are in an auditorium and then if you sing on the stage indirect sound is all the reverberation that is happening. There are many theaters/halls where it is very difficult to understand what is being said on stage. Because while you are about to hear second word, reflection of first word is reaching yoru hear. It makes sound all unclear. Such situations are solved by application of material on walls/ ceiling that can absorb noise.