Translation:A cup is broken
According to "a great user name"s explanation kinavunjika means more like "is breakable"
Hopefully someone will come along who has a brain that's currently working and can go into more depth (and correct me if my overtired brain has mucked it up).
Kuvunjika is the stative form of kuvunja. Kuvunjika is "to be broken", as opposed to the more action-y "to break".
Kikombe kimevunja is "a cup has broken", with the -me- being immediate past of break (I think).
Kikombe kimevunjika is "a cup is broken", with the -me- referring to entering the state of having been broken.
There's three verbs we can compare:
kuvunja "to break (something)" (active)
kuvunjwa "to be/get broken (by something/someone)" (passive) kuvunjika "to be broken/breakable" (stative)
Kuvunja and kuvunjwa both tell about an action.
Nimevunja kikombe. Kikombe kimevunjwa (nami). "I have broken the cup. The cup has been broken (by me)."
Kuvunjika is kind of similar to the passive but focuses on the state of the cup, rather than an action. There's a tendency for stative verbs to be interpreted as something-able when used with the present tense and something-ed when used with the perfect tense. As far as I know, that would look like this.
- Kikombe kinavunjika. "The cup is breakable."
- Kikombe kimevunjika. "The cup is broken."
The first one is a little bit like kikombe kinaweza kuvunjwa ("the cup can be broken") and the second one is a bit more like kikombe kimevunjwa ("the cup has been broken").
Some verbs with the stative suffix actually don't seem to be very "state-y" and are more "actiony", so I suspect a deeper linguistic analysis would possibly end up describing the -(i/e)ka verb ending as a mediopassive or something similar, which is like a passive but without any implied mention of the state (in this case, the state of being broken) being caused by another entity - which the passive does, even when the agent (causer) is not mentioned in the sentence.