Intrusive, meaning you don't wish to have them, and they distress you. You don't want these thoughts, and they bother you- which, in the case of OCD, means a person is more likely to keep thinking them: my harm thoughts scare me, so I worry about them, try not to think them....
It's a very fine skill, being able to not think about a thought, without thinking about it...
I believe the term for intrusive thoughts such as presents with 'pure-o', is 'egodystonic'.
The way I personally look at it, is my harm thoughts are not me; I don't want them; they do not reflect who I am as a person- that last one is hard to do, sometimes, because if I'm thinking them, I must be like that, right? It's hard- not saying what you have is OCD (sounds like it, though)- but it's hard with OCD, in my experience, to separate thoughts that come and go, from my core being.
I've read that everyone gets harm thoughts. Everyone think about hurting, killing, everyone gets that sudden urge to push their s/o off a cliff, if they happen to be standing on one. I find that hard to believe, but that's what they say. So, if that's the case, and yet we manage to get thru lives without acting on every violent impulse, then I remind myself that maybe I'm not so bad, after all.
I'm not going to worry about killing someone, until I do it- that's how I live with harm thoughts. And that takes a lot of the fright out of them, I refuse to worry, and I refuse to care about having the thoughts, and I refuse to worry that I might do it. If I do, I do. I've had these thoughts for 40+ years, and so far, I haven't. I'm not going to let these thoughts bother me any more than I have to, I think it's safe to say if I haven't acted on them in all this time, they're all bark, and no bite.