Insurance premiums usually increase each year because as you get older the chances of you dying or suffering from a serious accident or illness increase. This type of insurance is called Yearly Renewable Term Insurance (YRT).
Level term insurance is where the premiums you pay each month do not increase with age.
The best Level term cover is guaranteed to never increase. Premiums are fixed for the life-time of the policy which you can choose. At the start they will be more expensive compared to Yearly Renewable Term premiums, but by the time you're in your 50's your premiums will still be affordable while those with YRT policies will be thinking of cancelling, or reducing their cover, at the time that they are most likely to need to make a claim.
Visually this is represented by the graph on the right:
The "gold" bars represent the YRT premiums increasing with age and the "grey" bars the Level Term premiums staying the same.