What does dishonorably discharged from probation mean? Should I worry

It means you violated your probation too many times, now you will do jail time. Yes, be worried. Did you think you could screw them around indefinitely ?

Good question. "Dishonorable discharge" from the military is akin to a felony conviction. But, with respect to probation, "discharge" suggests that the probation is over. Tickle may be right, but the term is sort of oxymoronic, and leaves a lot to be desired.

Since a lot of time past since the conviction,I think you can apply for wavier.

The term is really not a common term for probation, where and what level probation may help.

But it appears obvious that probation has been violated, so it is not a good thing, and yes, I would be very worried

Since a lot of time past since the conviction,I think you can apply for wavier.

Where, exactly, did the OP mention any time passing?