Iambic just means that the poem is made up of lots of two-syllable units, in which the stress is placed on the second syllable. The lines also rhyme, although maybe not in the ways you'd expect.
"Rhyming Iambic Meter" makes the form and meter sound simpler than it really is. Coleridge could have sat down to write a standard iambic poem. If that were your project, there are a few ways to use rhyme and meter to let your readers know that's what you're doing. Ideally, your lines would all have the same number of iambic syllables. If they had four, we would call it "iambic tetrameter" if they had five, "iambic pentameter," and so on. But Coleridge didn't make this a normal poem. Check out the first section. Lines 1-7 have 8 syllables each, and lines 8-11 have 10 each, so it's a mix of tetrameter and pentameter.
Who cares exactly how long the lines are? Well, you might have been more likely to notice if you lived in the early 19th Century. You'd be more used to reading poets like Alexander Pope, who would rather chew off his arm than jump around like this in a poem. But we're willing to bet that you noticed this change in a subtle way, even if you didn't stop to count the syllables.
Think about the effects Coleridge can create with this technique. In the short lines at the beginning of the section, he's giving us a quick overview, and describing the rushing of a river to the sea. Then, as the poem slows down, the lines get longer too, and as we wind along those "sinuous rills," we start to feel the poem meandering a little too. When the setting changes in line 31 and the poem shifts gears, the lines get shorter again, back to the eight-syllable length. So the line lengths are a little weird at first, but when we look closer there's some logic to them.
Same goes for the rhyme – it isn't regular. Sometimes Coleridge loops back and picks up a rhyme he hasn't used in a while, creating a kind of echo in the poem. Remember that Coleridge is describing a drugged out dream here. Would it make sense to write it like a nursery rhyme? He creates strange music, where the different parts fit together in unexpected and beautiful ways.