IV is short for Individual Value. Every single pokemon has an IV between 0 and 31 for each of their individual stats; HP, Attack, Sp. Atk, etc... (ie: they have six different IV's in total). There is no easy method of knowing what your pokemon's IV's are. You can use an IV calculator (search Google) but you need to know things like how many EV's (Effort Values) you have accumulated through training etc for it to work.
IV's are determined as soon as you come into contact with a pokemon and CANNOT BE CHANGED!!! IV's essentially determine how strong one pokemon is in comparison to another pokemon of the same species. So, assuming the average IV is 15 or 16, an IV of 30 or 31 in say...Attack means that that particular pokemon's overall Attack stat will be higher than the average pokemon of its species. The same pokemon might have an IV of 0 or 1 or 2 in Speed, so it will be slower than the average pokemon of its species.
The effect of IV's does not become FULLY evident until a pokemon reaches lvl 100, but they do effect pokemon at all levels. At level 100, Pokemon A, who has an IV of 30 in Attack, will have an overall Attack stat that is 30 higher than Pokemon B, who is of the same species and has an IV of 0 in Attack.
At lower levels, the difference will not be so pronounced but it will still be there. For example, at lvl 50, Pokemon A will have an overall Attack stat that is 15 (half of 30) higher than Pokemon B.
The lower the level, the smaller the difference. At lvl 5, Pokemon A's Attack stat will only be greater than Pokemon B's by 1 measly point. But when you think about how weak a pokemon's stats are at level 5 (around 11 or 12 or so), that extra 1 point makes a fair bit of difference. The chance of finding a pokemon in the wild with IV's of 31 in every single stat is about 1 in 1,073,741,824 (according to my calc), so slightly worse than one in a billion. You can breed pokemon in order to get higher IV's but this is a very long-winded process and I probably wouldn't bother unless you were thinking of battling competitively.