I'd like to make a few notes:
1) Yes, 192.168/16 is reserved as a private address range along with 10/8 and 172.16/12 (RFC 1918).
2) The primary reason for the address changing is not security, though it can be a side effect. For that matter, my dynamic IP has remained constant for months. As SteveMann pointed out, it's a logistics issue of more nodes than possible IPv4 addresses. IPv4 addresses are 32 bits meaning 2^32 possible unique addresses. Some of these are reserved as private or special cases/uses (RFC 5735). This still leaves a large block of addresses that can be used as public where any node in the internet can address another publicly without masking or other tricks. However, with the explosion of modern day computers we have very quickly made more devices than the amount of available public addresses. With practically everyone being on the internet and usually having more than one device (such as a laptop and a phone) it quickly became apparent we would need far more addresses, especially with the anticipated explosion of IP devices. It's expected that soon all sorts of small devices will need their own IPs such as for surveillance or even your toaster. So IPv6 came around which uses 64 bits and dramatically increases the amount of possible unique addresses. The problem now is that the internet's infrastructure needs to update to support IPv6, which unfortunately isn't happening quickly enough. Until enough of the internet can support it the standard has to remain at v4. SteveMann explains why ISPs change addresses but there's an even bigger problem; the last IPv4 blocks have been issued (ICANN assigns its lastIPv4 addresses 3). That means every possible public IP is owned by someone. The main ICANN authority has divvied up its last blocks and now the regional registries are on their last v4 addresses and will have to recycle unused ones after exhausting those. So, major detour aside, IPv4 addresses are becoming a scarce commodity and need to be allocated from a finite size pool. Sometimes you get the same address back from your ISP, sometimes someone else gets that address.