Need a simple explanation of the inject method

You can think of the first block argument as an accumulator: the result of each run of the block is stored in the accumulator and then passed to the next execution of the block. In the case of the code shown above, you are defaulting the accumulator, result, to 0. Each run of the block adds the given number to the current total and then stores the result back into the accumulator. The next block call has this new value, adds to it, stores it again, and repeats.

At the end of the process, inject returns the accumulator, which in this case is the sum of all the values in the array, or 10.

Here's another simple example to create a hash from an array of objects, keyed by their string representation:

[1,"a",Object.new,:hi].inject({}) do |hash, item|
  hash[item.to_s] = item
  hash
end

In this case, we are defaulting our accumulator to an empty hash, then populating it each time the block executes. Notice we must return the hash as the last line of the block, because the result of the block will be stored back in the accumulator.

inject takes a value to start with (the 0 in your example), and a block, and it runs that block once for each element of the list.

1. On the first iteration, it passes in the value you provided as the starting value, and the first element of the list, and it saves the value that your block returned (in this case result + element).
2. It then runs the block again, passing in the result from the first iteration as the first argument, and the second element from the list as the second argument, again saving the result.
3. It continues this way until it has consumed all elements of the list.

The easiest way to explain this may be to show how each step works, for your example; this is an imaginary set of steps showing how this result could be evaluated:

[1, 2, 3, 4].inject(0) { |result, element| result + element }
[2, 3, 4].inject(0 + 1) { |result, element| result + element }
[3, 4].inject((0 + 1) + 2) { |result, element| result + element }
[4].inject(((0 + 1) + 2) + 3) { |result, element| result + element }
[].inject((((0 + 1) + 2) + 3) + 4) { |result, element| result + element }
(((0 + 1) + 2) + 3) + 4
10