Archaic means that a word has the flavor of old-timey language, and brings the feel of the past along with it. Archaic language is generally used infrequently and for effect when it is. I think that in English-speaking countries, the most common uses of archaic language are when religious texts are being quoted, or when older literature is being quoted--or performed, as in the case of Shakespeare or other period plays. Here's a fuller definition at Merriam-Webster.

Obsolete is a cousin of sorts to the word "archaic", and using an obsolete word will certainly make what you're saying seem esoteric and strange--but an obsolete word is a word that's no longer used at all. One should use such words with extreme caution: people listening to you or reading your writing may not know what you're talking about, unless you very carefully provide good context for them to figure out the meaning of what you're communicating. 

I wouldn't prioritize learning obsolete and archaic words until you get more advanced in English, and I don't think anyone's going to fault you for failing to know archaic words. 

If you want to take a crash course in archaic language, dipping into the plays of William Shakespeare would be a good start, as they are readily available, but prepare to be extremely bewildered! There exist translations of both of these with notes to explain the more perplexing turns of phrase. 

When should I use archaic and obsolete words?
Whenever I wake up my 2012 Macbook Pro after it's been asleep for a few hours, the screen turns on, but it is unresponsive for about a minute.  During this time, the mouse cursor does not move at all whenever I touch the trackpad and the computer is unresponsive to the keyboard.  I also see the WiFi icon in the taskbar act as if it is searching for WiFi (the WiFi icon is gray, but each bar turns black consecutively from bottom to top repeatedly).  The computer is finally responsive after a minute or so and the WiFi icon stops searching.  

Is this normal behavior for a Macbook Pro when waking?  If not, what could a potential issue be?  

My computer is a 2012 Macbook Pro 13 in, non Retina Display.  
