Orka literally means to have the energy or force to do something.
You almost always hear it in the negative sense, so jag orkar inte means 'I don't have the energy'. You'll also hear non-negated sentences, such as du måste orka (you have to find the energy) or hjälp mig att orka (help me find the energy), but even then there's usually an underlying sense that the activities are difficult.
Orka can refer to physical or mental energy, so jag orka inte springa (I don't have the energy to run) could mean the speaker physically cannot run or simply that they can't be bothered. You can use it with another verb (jag orkar inte städa/komma/prata – I don't have the energy to clean/come/talk) or on its own (jag orkar inte! – I don't have the energy!)
Its origins dates back to the Old Swedish that was used in the Middle ages (1225-1526), when the verb was first recorded. Orka exists and is used in this same way today in both Dutch and Icelandic.
In the past few decades, however, the Swedish word has also evolved into an interjection (Orka!), which is especially popular among teenagers and young people who use it in one-word sentences to express ‘couldn’t be bothered to’ or ‘can’t cope’.
Jag orkar inte gå ut ikväll.
I don’t have the energy to go out tonight.
Kan du ta ut soporna? Orka!
Can you take out the trash? I can’t be bothered!