"Blocking" means that the caller waits until the callee finishes its processing. For instance, a "blocking read" from a socket waits until there is data to return; a "non-blocking" read does not, it just returns an indication (usually a count) of whether there was something read.
You hear the term mostly around APIs that access resources that don't necessarily require CPU attention -- I/O, for instance. You also hear it in multi-threading: A call from Thread A to Thread B might be designed to "block" (hold up Thread A) until Thread B achieves the relevant state to process or at least accept the request. (The most obvious example there being "join", which usually means "I, Thread A, want to wait until Thread B has terminated" -- you use that when exiting a multi-threaded program.)
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