Conditioning Legs.
In Karate to be able to execute great Kicks and perform deep and solid stances the first step is Flexibility. Please see the tab on Flexibility and spend a large part of you training on you flexibility during class might not be enough and therefore you must spend necessary extra time working on been as flexible as you can.
Been able to deliver explosive kicks and be able to move and transition form position to position will be easer if the practitioner is very limber. Flexibility is not just the ability to do a split but also many stretching abilities. Loose ankles, knee joints and hips are key but, will take years of hard work. Once the goal is achieved maintaining this status is key and it must be worked consistently or you will loose this ability.
After the flexibility comes strength, there are many conditioning drills and exercises that will strengthen the legs. The key is to understand the workload that you are trying to achieve example: A competitor might spend more time with plyometric exercises that a practitioner that is just interested in the Budo aspect of Karate.
If you are a competitor please spend some time on the tab for plyometrics and come up with a routing that fits you, remember that consistent training is the key as the work that you are doing will help convert your muscles from slow twitch to fast twitch and stopping the training will make the muscles revert to original state.
The most important is consistency and if you want to be a good kicker you must be very flexible.