What does the Korean term imply, and how is it used?

Although the character 각 originally meant "angle," it's now commonly used (in colloquial language) to indicate "It seems like a great fit/timing for" anything.
Billiard games (당구) are credited with giving rise to this name, as you can hit the balls from certain "angles" that are advantageous. Thus, in situations where you have a decent angle, you say 각이 나온다; in situations where you don't, it's 이 안 나온다.

How do you use it in a sentence?

• You use a noun and then just add 각 and say the 이다 verb ([noun]각이다) and conjugate it accordingly.   

Examples

• If you think that's a good time to have fried chicken (or if you just need an excuse), you can say 치킨각. (이거 치킨각인데?)
• If you filmed a short video that would be great or popular on TikTok, you can say 틱톡각. (이거 틱톡각인데? / 이거 틱톡각 아니야?) 

The usage can be literally limitless because you can put 각 after any noun, but you need to be careful because if you use this word too much, you will sound too casual and sometimes rude in certain situations.