As to what the Broadcast address *is*, it's actually surprisingly simple, but perhaps a little tricky to explain.
Many network media types - a good example is Ethernet - have a broadcast facility, which allows one station (computer wth a network card) to send a frame (in our case, holding an IP packet) that's intended to be received by every connected station.
Normally, you only send an Ethernet frame to one particular station, using an Ethernet address, which is also known as a MAC address. Your computer gets these from IP addresses by using a protocol called ARP.
But if you want to send - using IP - a packet to all computers on your IP network, then we need to set aside a special address that all the computers agree on, which gets translated to the special Ethernet broadcast address.
This *used* to be traditionally the "all zero" address - that is, all the bits in the subnet part of the IP address were all zeros - but this was switched some time ago to be the "all ones" address.
Hence on what used to be a class C, now known as a /24, the last number of your broadcast address will indeed be "255". Each number is 8 bits long, by the way, and is known as an "octet". On a /25 address, half the size of a /24, the broadcast address is still "all ones", which means it's likely to be either "255" or "127", depending on which half you have.
Thankfully, because these things are rather easier for computers to calculate than humans, there's copious tools to do it.
For instance, on RedHat, you needn't enter the broadcast address at all - you always need the netmask (which is, actually, that /24 or /25 or whatever in a different notation) - and it'll figure out the broadcast based on that, using ipcalc:
[root@turner root]# ipcalc 192.168.0.2 255.255.255.192 -b
[root@turner root]# ipcalc 192.168.0.2/26 -b
Just as a last tip:
If you know the netmask, but need that /24 style - known as a "prefix length" or "CIDR notation" - then ipcalc will also do this for you, and vice versa. Try the above examples using "-p" and "-m" instead of (or as well as ) the -b.