This circuit is an astable multivibrator, or oscillator. The two transistors are cross-coupled in such a way that the circuit switches back and forth between two states. In one state, the base of Q1 is about one diode drop above ground, allowing a base current to flow. This keeps Q1 switched on, in saturation mode, allowing a current to flow through the collector, keeping Q1's collector voltage low, and discharging C1. Q2 is switched off, because its base voltage is not high enough to switch it on.
As the collector current into Q1 flows through C1, the base voltage for Q2 goes up, until it is high enough to switch on Q2, causing a current to flow through its collector, which drops the collector voltage (the current causes a voltage drop across the resistor above it). The right side of C2 has dropped, but the voltage across it hasn't changed, so this causes Q1's base voltage to drop below ground, switching it off.
Then we get the other half of the cycle, with current flowing through Q2. This continues until Q1 turns on, and then the cycle repeats.
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