Oral posture is a fancy term for the way your speech muscles (lips, jaw, tongue, soft palate, etc.) move to shape your sounds, or your vowels and consonants, as you talk. Different accents have different oral postures, which is why they sound different.
If you are trying to change your accent and you can figure out another accent’s oral posture and how to shift into it with your speech muscles, it helps you stay consistent in a much easier way. Oral posture is such a helpful tool if you feel you have a ‘bad ear’ or if you feel like you keep slipping in and out of the accent but don’t know why. With this tool, you don’t have to hear yourself, (which isn’t helpful anyway!) because you will have a way of feeling your way into the accent.
Feeling is more reliable than hearing when trying to shift accent, because your ear will play tricks on you. Linguists call this ‘phonological interference’— when we hear a foreign accent or language, our tendency as humans is to hear it in terms of the sounds of our own accent or language, and so we speak that accent or language using our own sounds. This is totally unconscious, and can be very frustrating when trying to learn a new accent! So let’s totally sidestep it and instead, focus on the feeling of the accent. This is what ‘oral posture’ allows us to do.