I have no #*@#& idea what the word means. In poetry or in any other genre. I know what it used to mean to me — murky and irritating. Is Milton profound? Maybe, but the way he bullied his daughters into being his secretaries is more interesting.
Is profundity depth and insight, or is it difficulty? More often than not it’s just the latter. And often it’s difficulty for its own sake. I’ve worked with poets who were proud because every poem was Sisyphean. They took great delight in having people work hard to guess the poem’s putative meaning. Or — and this is worse somehow — “It can mean whatever the reader needs it to mean.” At that point I usually passed out and hit my head on the desk.
My advice (since you asked) is to forget about Meaning and its ugly step-sister Profundity and just write. Here’s a familiar anecdote — a guy goes to a guru and says, “I’m going to work in a vegetarian restaurant but I don’t want to forget my spiritual practice.” The wise man (or maybe wise guy) says, “When you wash the peas, wash the peas.” “Fine. Right. But I don’t want to forget my spiritual practice.” A which point the guru hit him with a stick.
So unless you want me to come to your house and hit you with a stick, wash the peas. If there’s even one little speck of profound grit left in there, I’m going to be mad.