It can be useful to understand binary when coding, since data is all represented in binary and all operations are done on binary values. Computers don't work with data in decimal, and this can lead to some surprises if you don't understand how binary works.
One of the most direct uses of binary you may encounter in coding is in the implementation of flags, or simple true/false values. Often, instead of having a separate variable or boolean for each possible true/false option, the values will be combined via a larger data type. You can represent eight different true/false values with a single byte and then extract the value of each by ANDing the combined value with a 1 in the appropriate bit.
It can also be very important in overflow situations. If you are working with a char data type in c++, and have the value of 129, which is 10000001 in binary, if you double that you will get 2, because in binary you end up with 100000010, but a char can only hold 8 bits so you lose the leftmost 1 and get 00000010 or 10 which is 2.
In any case, understanding the mechanics of what's going on will help in the long run, and probably save on some headaches down the road.