‘For there is no faithfulness (steadfastness) in their mouth,
Their inward part is destructions (or ‘a yawning gulf'),
Their throat is an open sepulchre,
They flatter with their tongue.'
He describes his enemies, those who are against him and against YHWH. He declares that what they say cannot be trusted, that their inner thoughts plan destruction for others, and especially for the people of God, that their throat is like an open grave i.e. what they say may result in death for the unfortunate so that they enter the open grave, or may lead to ruin. And yet at the same time they speak smooth words with their tongues. They are totally untrustworthy.
Alternately behind the idea of the open sepulchre might be the idea of a grave that has been opened and the stench of a rotting body rises from it. So are the lives of these wicked men, they stench rottenly, and those who have contact with them become unclean.