Understanding the geometrical interpretation of word2vec
If two words tend to appear in the same context, then they will tend to receive a similar word vector.

For instance, a large corpus might contain sentences like "I really love Fuji apples" and "I really love Gala apples".  From this we can see that "Fuji" and "Gala" have appeared with the same context (in this case the context is "love _ apples", if by context we look one word to the left and one word to the right).  This will tend to cause the optimization algorithm to assign Fuji and Gala vectors that are similar.

As you can see, words that tend to be associated with the same surrounding context will often have a similar semantic content.  Not always, but it's a good heuristic.