Definition of bilateral
By "bilateral" we mean a print that can touch both sides, from above and from below. If this is still not perfectly clear to you, nothing better than an example. You receive 4-5 preflop. If the flop comes 6-7-x or 2-3-x, you will have a two-sided straight draw. In the first case, a 3 will give you the big straight and an 8 will give you the small straight. In the second example, same principle, you can complete your small straight with the 5 or your big straight with the ace.
The importance of distinguishing between small and large fifths
In our example above, we say that with 4-5 over 6-7-x, we would have a big straight if a 3 fell on the turn and a small straight if an 8 fell on the turn. The reason being that the big straight will give us the best possible straight. On 6-7-x-3, the best straight is made with 4-5. But if you have 4-5 on 6-7-x-8, your straight would be beaten by 5-9 or 9-10. The two-sided draw increases our chances of completing it. With 4-5 over 2-6-J you have 4 cards that can give you a straight (all four 3s for a non-bilateral draw) whereas if the draw is bilateral as in 5-6-x, you will be helped by 8 cards!