[chryuop]

It is not really the same thing, but let me try with this example. You are studying English, what you call the place where someone lives? DO you need to learn only home or you need to learn house too?
Now, as I said the example is not really the same thing, but I think it might help you to understand.

As e general guideline I would say the On-yomi it is used to form compound kanji, while kun-yomi you will mostly find them as stand alone words or to form Japanese names. But this is very very summerized since there are tons of exceptions. If you take for example tha kanji 火 (fire), where the On-yomi is カ and the kun-yomi is ひ and ほ, when it is taken alone (as far as I know) it is always pronounced ひ, while か only in compound. But if you consider 足 you will find it with its kun readings as stand alone as あし (foot/leg), たる/たりる (be enough) or たす (to add). But you will also find its onyumi as stand alone ソク since it is the counter for foot wears.

As you can see by this little example you need to know both readings...but the problem is not if you need to know both, but how you get to know them.
There are 2 main "schools" of thoughts about it. Some people prefere learning only the readings they meet when they do exercises, read book, newspapers and so on. Some people prefere taking the list of the most used kanji and learn by heart all readings for each kanji. There are pro and cons for both way of learning, so up to you to pick which one you prefere.