What does it mean to "swamp" a radio signal?
swamp

swɒmp

noun


an area of low-lying, uncultivated ground where water collects; a bog or marsh.
synonyms:   marsh, bog, quagmire, mire, morass, fen, quag, sump; More


verb


overwhelm or flood with water.
"a huge wave swamped the canoes"
synonyms:   flood, inundate, deluge, wash out, soak, drench, saturate, immerse
"the rain was driving down with great force, swamping the dry ground"


Source: Lexico.



You're using the verb and "overwhelm" is a good alternative. In the context of radios the signal is so strong that the receiver can't see the modulation (AM or FM) any more and reception is lost.



Figure 1. An AM radio demodulation circuit. Image from What role does the capacitor play in an AM demodulating circuit?.

This is a very crude example but it may help. It should be clear from Figure 1 that the diode and capacitor are demodulating the incoming modulated RF signal. If the demodulator stage was preceded by an amplifier stage then it would be possible for a very strong incoming signal to drive the amplifier into saturation so that (what were) the low amplitude RF cycles are amplified to the same level as the peak amplitude signals. When that happens the modulation has been lost and the demodulation stage will just give a DC output and no audio. In the case of the AM radio one could expect the audio to be distorted as the signal level goes from "acceptable" to "swamped" as the positive peaks get increasingly clamped until eventually the modulation drops to zero.