This expression is useful for the following situation:

• There's something specific which you want.
• You can't get it.
• You can get something else instead, which is not as good but is OK.

For example, if you really want some vanilla ice cream, but you don't have any, you can eat a cookie instead and think:

Well, it's not ice cream, but it's better than nothing.

Sometimes "___ is better than nothing" can be shortened to just "Better than nothing."