Not referring to the definition in the dictionary. In the context of blockchains and Ethereum in particular, the term "grief" has been used repeatedly in a host of scenarios: ethresear.ch, Plasma calls, Twitter conversations etc.
This question is about the verb "to grief" rather than the noun "grief".
The latter is presumably what lots of people are currently feeling due to the drop in cryptocurrency prices.
The former, which is what you're asking about, is when someone uses a system in an unexpected way to create what other users of the system might call an attack. Such an attack doesn't benefit the attacker, but does make using the system more difficult for the victim. (i.e. It causes them grief [noun].)
It's a common term in computer games, where the person performing the griefing is referred to as the griefer.
For an example in the Ethereum world, take a look at the Insufficient Gas Griefing attack.