Direct coupled refers to coupling between stages of an amplifier and coupling of the output stage to the load.
The reason for coupling devices between stages is to accommodate the different DC biases needed by each stage.
Normally you can't just connect the collector output of one stage to the base input of another identical stage, since collector and base operate at very different voltages. So an interstage transformer or capacitor provides DC isolation between stages while passing the audio.
Direct-coupled interstage designs often use complementary stages; a PNP transistor drives an NPN transistor, etc. This makes it much easier to obtain bias compatibility between stages. See ref, figure 2.5.
Direct output coupling is used to eliminate the nonlinearity, phase-shift and limited frequency response of a transformer or capacitor.
The drawback is the possibility of applying a DC bias to the load.
Direct output coupled amplifiers usually have a bias nulling adjustment which may need occasional adjustment.