The meaning seems to be that Sennacherib feels himself able to cope with any difficulty. Mountains do not stop him, he climbs over them. Deserts do not stop him, he crosses them, digging his own wells for water. Rivers do not delay him, they dry up underneath his feet.
Rivers of besieged places.
Perhaps a reference to Egypt. Egypt was beyond the desert and was cut up by many canals. Sennacherib was making the boast that these would prove no obstacle to him, they would simply vanish before him.