Flashback! It's going to be important to keep track of these time shifts, because there are a lot of them.
The speaker recalls a time when he used to press his face to the glass of the tanks at the aquarium.
We can assume this took place a while ago, when it was open, perhaps when he was a child and completely enthralled by the passing fish.
"Like a snail" describes his nose up against the glass. It's an interesting simile (kinda gross, but interesting) because it makes us think of what might be on the inside of the tank in its directly opposite environment (the outside where the onlookers are).
my hand tingled to burst the bubbles drifting from the noses of the cowed, compliant fish.
The speaker is still remembering the excitement of being at the aquarium. He was so captivated that he wanted to reach in a pop the bubbles coming from the mouths of the fish.
To describe the fish as "cowed" and "compliant" is to suggest that they have been forced or intimidated into this position—which is, in a way, true. They didn't choose to be put in an aquarium for observation. (What fish would, we wonder…)
For Lowell to make this judgment about the oppression of the fish might mean he's gearing up to take this small scene and blow it up into a bigger picture. So heads up, gang.
In lines 7 and 8 Lowell has a little fun with alliteration. He repeats the B sound in "burst" and "bubbles," and the hard C sound in "cowed" and "compliant." This has a somewhat musical effect that carries into the poem.