Think of ISDN as a "digital phone line." An ISDN line is made up of two unique 64Kb/s channels which can be combined together to form a single 128Kb/s circuit. There's also another channel on the ISDN that's used for signaling. ("Hey, line #2 is ringing" or "send a busy signal if you just called line #1 - It's in use" since there are no electrical signals like you have on a regular phone line that handle busy signals and rings. ISDN lines must be dialed and be answered by another ISDN line or a special circuit (called a PRI, a bundle of ~11 ISDN lines combined together) when used for data. In short, think of it as a special and faster dial-up modem.
A leased line is a dedicated circuit - An extension of your network that must be controlled by CSU/DSU's (which kind of act like modems but there's no dialing involved) and typically routers. They are always always connected. Common leased lines are old and slow 64Kb/s circuits, T1's (1.5Mb/s) and DS3's (also called T3's) at 45Mb/s. T1's and DS3's can also be "fractional" where you buy the circuit in chunks - A T1 is made up of 24 64Kb/s lines (Noticing a trend here?). You can buy a half of a T1 at 768Kb/s, a 256Kb/s fractional T1, a 1024Kb/s fractional T1, etc. A DS3 is made of 28 T1's, and it can also be purchased in fractions.
There are some other types of leased lines, and the definition is somewhat blurry. 64K/T1/DS3 are the "classic" ones, but DSL is definitely in the same general territory - Always on, dedicated connection, etc. A cable modem is different - It's more like an Ethernet network run over your cable system.
Because I can't stand to just dump this information on you without something to tie it all together..
A T1 is a "bundle" of 24 channels. These can either be used for data (Each channel is 64Kb/s) or a single normal voice line like you have at your house. A DS3 is a bundle of 28 T1's, meaning 45Mb/s or 672 voice lines. ISDN is similar. A PRI is just like a T1, except it only has 23 channels that are useable - The 24th is used for signaling.
Hope this helps!
- G