Kinda. That's the subnet mask, which is a representation of how big the subnet is. A mask of 255.255.255.0, which is also known as a /24 subnet (which is the newer CIDR notation) or a class C subnet (which is technically inaccurate but network people will know what you mean), can contain up to 254 hosts - 1-254 (the top and bottom address are always reserved for broadcast and the "network address", respectively, but technically they are part of the network so there are 256 IPs in a /24 subnet - just not ones you can use).

If you want to look at how it really works, the CIDR notation is the most intuitive. An IP address isn't really four numbers - it's one number. The address I get for Google is 173.194.33.16, or 2915180816 (nobody really uses decimal notation except as a joke), or 10101101110000100010000100010000 in binary. The four number notation is called a "dotted quad". The subnet mask specifies the number of bits that are the network part - the street name - as opposed to the host part - the house number.

A network mask of 255.255.255.0 or /24 is 11111111111111111111111100000000 in binary. That means that the first 24 bits (or the first 3 octets - which happen to correspond to parts of the dotted quad) are the network part. Assuming the Google IP above is on a /24 network, this is what it would look like with the network part in bold:

• 173.194.33.16
  
• 10101101110000100010000100010000
• (I can't do this with the decimal notation as decimal digits don't correspond to binary sanely - thus why nobody uses it)

Now, I don't know if that IP is on a /24 network. I don't have to - I know it's not on my network, so I send it to a router and that figures out where it goes from there. Odds are nobody but Google knows whether that's on an actual /24 network - companies usually purchase a large subnet from ARIN or their ISP and then advertise a route to that large subnet (say a /16, if Google owns 173.194.0.0/16 - which is 256*256 IPs or 2¹⁶ ) and route the smaller ones internally.

Networks don't only come in /8, /16, and /24 (one octet, two octets, and three octets of network part respectively), but they're the simplest to deal with visually, so they're usually used. Most home routers use a /24 network cut out of the 192.168/16 network, which is reserved for "private" IP space, or space that isn't routed on the Internet.

Oh, uh, a lot of this changes in IPv6 :) But the core concepts are the same.