I've read a book on computer networks, and among other subjects the author touched WiFi security. It was said that WiFi has some serious security flaws and that there is even free publicly available software for WiFi snooping. The protocol in use was WEP, but was replaced in 2004 with something more secure (didn't cover that). So the question still remains, how secure is wireless traffic nowadays if access point requires password (and the intruder doesn't know it)? And how to check if my access point device in LAN is indeed transmitting and receiving securely?
"How Secure?" is a difficult question to answer. It depends on your particular circumstance and risk tolerance.
If you are using WPA2 for encryption with a complex key, than I think it's reasonable to say that your connection is at least as secure as a wired Ethernet connection.
Nothing can be 100% secure these days. There was a case back in 2011 where a WiFi neighbor Barry Ardolf, 46, repeatedly hacked into his next-door neighbors’ Wi-Fi network to frame them for child pornography and other horrendous misconduct. Last year in Japan, a Wi-Fi router was attacked. Generally WPA2 is considered more secure than its predecessor WEP but there are Reaver exploits that can crack this easily.