# your mouth will be opened up

"I will open your mouth" or "I will cause you to know what to say"

# you will speak—you will no longer be silent

These phrases mean that Ezekiel will speak. In the second phrase it is stated in negative form to emphasize that he will speak.

# You will be a sign for them

"You will be a warning for them". See Ezekiel 12:6. 

# know that I am Yahweh

"understand that I am Yahweh, the one true God". Yahweh implies that they will know that he is the one true God who has supreme authority and power. See Ezekiel 6:7.